• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.791-800
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• 1998

We present a proof that, among all complex numbers, Duffin-Schaeffer's choice in the Neumann series expansion of the inverse of a frame operator has the best possible convergence rate.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.87-97
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• 2013

The purpose of this paper is to employ a new useful technique to solve the initial-Neumann boundary value problems for parabolic, hyperbolic and parabolic-hyperbolic equations and obtain a solution in form of infinite series. The results obtained indicate that this approach is indeed practical and efficient.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1511-1528
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• 2020

A skew generalized power series ring R[[S, 𝜔]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action 𝜔 of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain some necessary conditions on R, S and 𝜔 such that the skew generalized power series ring R[[S, 𝜔]] is (uniquely) clean. As particular cases of our general results we obtain new theorems on skew Mal'cev-Neumann series rings, skew Laurent series rings, and generalized power series rings.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• Ocean Systems Engineering
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• v.7 no.4
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• pp.371-398
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• 2017

Calm water wave resistance plays a very important role in ship hull design. Numerical methods are meaningful for this reason. In this study, two prevailing methods, the Neumann-Kelvin and the Rankine source method, were implemented and compared. The Neumann-Kelvin method assumes linearized free surface boundary condition and only needs to mesh the hull surface. The Rankine source method considers nonlinear free surface boundary condition and meshes both the ship hull surface and free surface. Both methods were implemented and the wave resistance of a Wigley III and three Series 60(Cb=0.6, 0.7, 0.8) hulls were analyzed. The results were compared with experimental results and the merits of both numerical techniques were quantified. Based on the results, it is concluded that the Rankine source method is more accurate in the calculation of the wave-making resistance. Using the Neumann-Kelvin method, it is found to be easier to model the hull and can be used for slender ships to solve problems like wave current coupling calculation.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.721-745
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• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.877-880
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• 1999

A rigorous formulation is suggested〔l,2,3〕 in solving the scattering of plane waves by a dielectric wedge. Correcting surface currents are expanded in a Neumann series of fractional orders to meet the edge condition of static limit〔4〕. For the better converging series, the modified Neumann series satisfying the static limit edge condition and the radiation condition are suggested here for the surface currents having two different wave numbers of air and dielectric〔4〕. This representation gives accurate solutions over the whole region including the grazing incidence of the plane waves upon the dielectric wedge of large permittivities.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.593-600
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• 2003

Structural optimization often requires the evaluation of design sensitivities. The Semi Analytic Method(SAM) fur computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements. the SAM shows severe inaccuracy. In this study, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover. the error of the SAM caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally the present study shows that the refined SAM including the iterative method improves the results of sensitivity analysis in dynamic problems.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.9
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• pp.1027-1038
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• 1988

This paper, the last part of these three companion papers treated the electromagnetic diffraction by a dielectric wedge, presents the correction to the physical optics approcomation by the sheet currents of the Neumann expansion. Those expansion coefficients obtained by solving dual series equation amenable to simple numerical calculation may provide the asymprotically corrected solution. The validity of this result, satisfying both the edge condition near the tip of the dielectric wedge and the boundary condition along dielectric interfaces, is assured by approach of the corrected diffraction pattern to that of a perfectly conducting wedge for large permittivity of dielectric wedge.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.2
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• pp.1-10
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• 1987

The wave resistance of ships is calculated with the numerical solution of the Newmann-Kelvin problem. For the sake of the numerical evaluation of the Green function, Shen and Farell's method is used[7]. In particular, the contribution of the line integral term in the Neumann-Kelvin problem to the calculated values of the wave resistance is shown. For the Wigley's hull the calculated values of the wave resistance and the wave profiles at the hull surface are in fairly good agreement with the experimental data. However, for the series 60 hull and the practical hull, a 454,000 cubic feet reefer vessel, the calculated results of the wave resistance show definte hollows and humps considering the experimental result.