• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.493-498
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• 2004

In this paper, we try to construct the variation of the Green's function and investigate some operator properties of the Green's function. Also, we discuss the variation of the operator of the Green's function G(x, t) when the operator is varied.

• 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.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.777-786
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• 2014

We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.337-353
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• 1994

Let H be a Schrodinger operator in $L^2$(R) H =(equation omitted) ＋ V(x), with supp V ⊂ [-R, R]. A number $z_{0}$ / in the lower half-plane is called a resonance for H if for all $\phi$ with compact support 〈$\phi$, $(H - z)^{-l}$ $\phi$〉 has an analytic continuation from the upper half-plane to a part of the lower half-plane with a pole at z = $z_{0}$ . Thus a resonance is a sort of generalization of an eigenvalue. For Im k > 0, ($H - k^2$)$^{-1}$ is an integral operator with kernel, given by Green's function(omitted)

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• Advances in nano research
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• v.7 no.3
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• pp.209-221
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• 2019

Graphene, with impressive electronic properties, have high potential in the microelectronic field. However, graphene itself is a zero bandgap material which is not suitable for digital logic gates and its application. Thus, much focus is on graphene nanoribbons (GNRs) that are narrow strips of graphene. During GNRs fabrication process, the occurrence of defects that ultimately change electronic properties of graphene is difficult to avoid. The modelling of GNRs with defects is crucial to study the non-idealities effects. In this work, nearest-neighbor tight-binding (TB) model for GNRs is presented with three main simplifying assumptions. They are utilization of basis function, Hamiltonian operator discretization and plane wave approximation. Two major edges of GNRs, armchair-edged GNRs (AGNRs) and zigzag-edged GNRs (ZGNRs) are explored. With single vacancy (SV) defects, the components within the Hamiltonian operator are transformed due to the disappearance of tight-binding energies around the missing carbon atoms in GNRs. The size of the lattices namely width and length are varied and studied. Non-equilibrium Green's function (NEGF) formalism is employed to obtain the electronics structure namely band structure and density of states (DOS) and all simulation is implemented in MATLAB. The band structure and DOS plot are then compared between pristine and defected GNRs under varying length and width of GNRs. It is revealed that there are clear distinctions between band structure, numerical DOS and Green's function DOS of pristine and defective GNRs.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• The Journal of Korea Robotics Society
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• v.15 no.3
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• pp.293-300
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• 2020

The purpose of our sensor system is to transparentize the large hydraulic manipulators of a six-ton dual arm excavator from the operator camera view. Almost 40% of the camera view is blocked by the manipulators. In other words, the operator loses 40% of visual information which might be useful for many manipulator control scenarios such as clearing debris on a disaster site. The proposed method is based on a 3D reconstruction technology. By overlaying the camera image from front top of the cabin with the point cloud data from RGB-D (red, green, blue and depth) cameras placed at the outer side of each manipulator, the manipulator-free camera image can be obtained. Two additional algorithms are proposed to further enhance the productivity of dual arm excavators. First, a color correction algorithm is proposed to cope with the different color distribution of the RGB and RGB-D sensors used on the system. Also, the edge overlay algorithm is proposed. Although the manipulators often limit the operator's view, the visual feedback of the manipulator's configurations or states may be useful to the operator. Thus, the overlay algorithm is proposed to show the edge of the manipulators on the camera image. The experimental results show that the proposed transparentization algorithm helps the operator get information about the environment and objects around the excavator.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.425-440
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• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.