• East Asian mathematical journal
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• 제38권1호
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• pp.33-41
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• 2022

In this paper, we study singular Dirichlet boundary value problems involving ϕ-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity f = f(u) has a positive falling zero and is either superlinear or sublinear at u = 0.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권2호
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• pp.97-111
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• 2011

We provide a semilocal convergence result for approximating a solution of a singular system with constant rank derivatives, using Newton's method in an Euclidean space setting. Our approach uses more precise estimates and a combination of two Lipschitz-type conditions leading to the following advantages over earlier works [13], [16], [17], [29]: tighter bounds on the distances involved, and a more precise information on the location of the solution. Numerical examples are also provided in this study.

• 디지털산업정보학회논문지
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• 제8권4호
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• pp.115-120
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• 2012

In multi-user multi-input multi-output (MU-MIMO) system, zero forcing beamforming (ZFB) is regarded as a realistic solution for transmitting scheme due to its low complexity and simple structure. However, ZFB shows a significant performance degradation when channel matrix has large condition number. In this case, the largest singular value of the channel inversion matrix has a dominant effect on transmit power. In this paper, we propose a perturbation method for reducing an effect of the dominant singular value. In the proposed algorithm, channel inverse matrix is first decomposed by SVD for the transmit signal to be expressed as a combination of singular vectors. Then, the transmit signal is perturbed to reduce the coefficient of the singular vector corresponding to the largest singular value. When a number of transmit antennas is 4, the simulation results of this paper shows that the proposed method shows 8dB performance enhancement at 10-3 uncoded bit error rate (BER) compared with conventional ZFB. Also, the simulation results show that the proposed method provides a comparable performance to Tomlinson-Harashima Precoding (THP) with much lower complexity.

• 호남수학학술지
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• 제38권3호
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• pp.661-674
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• 2016

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.501-515
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• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 봄 학술발표회 논문집
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• pp.35-42
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• 1997

The two-state or mutual M-integral which is derived from tile M-integral and is applicable for two elastic states, is applied for computing all intensity of a singular near-tip field around the vertex of a class of wedge, encountered in adhesive lap joints under mechanical loading. Numerically we verify that a simple auxiliary field associated with every eigenfunction for the composite wedge under consideration exists in the form of the conjugate solution in the sense of tile M-integral. The auxiliary field is then employed for superposition with the elastic field under consideration, and the associated two-state M-integral is computed via the domain integral technique. This enables us to extract the intensity for a singular field information for a singular elastic boundary layer is extracted form the domain integral representation without resort to singular finite element for the wedge vertex.

• Steel and Composite Structures
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• 제6권4호
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• pp.353-366
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• 2006

The discrete singular convolution (DSC) algorithm for determining the frequencies of the free vibration of single isotropic and orthotropic laminated conical shells is developed by using a numerical solution of the governing differential equations of motion based on Love's first approximation thin shell theory. By applying the discrete singular convolution method, the free vibration equations of motion of the composite laminated conical shell are transformed to a set of algebraic equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. The obtained results are in excellent agreement with those in the literature.

• International Journal of Computer Science & Network Security
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• 제21권12호
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• pp.223-227
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• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.

• East Asian mathematical journal
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• 제34권5호
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• pp.623-632
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• 2018

In [7, 8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.