• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.669-674
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• 2022

In this paper, we shall consider some properties of the metric projection as a set valued mapping. For a set G in a metric space E, the mapping 𝜋_G; x → 𝜋_G(x) of E into 2^G is called set valued metric projection of E onto G. We investigated the properties related to the projection P_S(·)(·) and 𝜋_S(·)(·) as one-sided best simultaneous approximations.

• 대한수학회보
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• 제26권2호
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• pp.191-201
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• 1989

In this article we are interested in characterizing when metric projection is Lipschitz continuous and determining when metric selections which are also Lipschitz continuous exist.

• Structural Engineering and Mechanics
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• 제38권3호
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• pp.261-281
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• 2011

A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

• 한국통신학회논문지
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• 제40권7호
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• pp.1257-1265
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• 2015

본 논문은 투영 행렬을 이용한 높은 채널 용량을 획득할 수 있는 사용자 선택 기법을 제안한다. 기존의 Frobenius norm기반의 사용자 선택 기법이 다수의 사용자를 선택할수록 정확도가 감소하는 점을 투영 행렬의 근사화 형태를 이용하여 개선하였다. Flop count를 이용한 제안 기준의 계산복잡도를 분석하였고, 모의 실험을 통하여 안테나 구성에 따른 획득 가능한 채널 용량에 대해서 비교하였다. 모의 실험 결과를 통해 제안한 사용자 선택 기법이 더 높은 채널 용량을 획득하는 것을 확인하였다.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.615-626
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• 2019

The 3-noded metric Timoshenko beam element with an offset of the internal node from the element centre is used here to demonstrate the best-fit paradigm using function space formulation under locking and mesh distortion. The best-fit paradigm follows from the projection theorem describing finite element analysis which shows that the stresses computed by the displacement finite element procedure are the best approximation of the true stresses at an element level as well as global level. In this paper, closed form best-fit solutions are arrived for the 3-noded Timoshenko beam element through function space formulation by combining field consistency requirements and distortion effects for the element modelled in metric Cartesian coordinates. It is demonstrated through projection theorems how lock-free best-fit solutions are arrived even under mesh distortion by using a consistent definition for the shear strain field. It is shown how the field consistency enforced finite element solution differ from the best-fit solution by an extraneous response resulting from an additional spurious force vector. However, it can be observed that when the extraneous forces vanish fortuitously, the field consistent solution coincides with the best-fit strain solution.

• 충청수학회지
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• 제28권3호
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• pp.473-482
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• 2015

Let Qf be the maximal derivative of f with respect to the Bergman metric $b_B$. In this paper, we will find conditions such that $(1-{\parallel}z{\parallel})^s(Qf)^p(z)$ is bounded on B. We will also find conditions such that Bergman projection type operator $P_r$ is bounded operator from $L^p(B,d{\mu}_r)$ to the holomorphic Besov p-space Bs $B^s_p(B)$ with weight s.

• East Asian mathematical journal
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• 제28권3호
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• pp.305-320
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• 2012

The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

• 대한수학회지
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• 제27권2호
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• pp.211-221
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• 1990

• 대한수학회보
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• 제33권1호
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• pp.65-73
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• 1996

• ETRI Journal
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• 제35권6호
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• pp.1115-1125
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• 2013

This paper presents a scheme for geometric correction of projected content for planar and quadratic projection surfaces. The scheme does not require the projection surface to be perfectly quadratic or planar and is therefore suitable for uneven low-cost commercial and home projection surfaces. An approach based on the recursive subdivision of second-order B$\acute{e}$zier patches is proposed for the estimation of projection distortion owing to surface imperfections. Unlike existing schemes, the proposed scheme is completely automatic, requires no prior knowledge of the projection surface, and uses a single uncalibrated camera without requiring any physical markers on the projection surface. Furthermore, the scheme is scalable for geometric calibration of multi-projector setups. The efficacy of the proposed scheme is demonstrated using simulations and via practical experiments on various surfaces. A relative distortion error metric is also introduced that provides a quantitative measure of the suppression of geometric distortions, which occurs as the result of an imperfect projection surface.