• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.849-862
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• 2011

In this paper, we introduce certain concepts which provide us with a perspective and insight into the generalization of orthogonality with the normalized duality mapping. The material of this paper will be mainly, but not only, used in developing algorithms for the best approximation problem in a Banach space.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.303-305
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• 1993

Walsh function and transform are important analytical tools for control theory and signal processing and have wide applications in those fields, especially in the field of digital communications. Therefore there is a need for a Walsh function generator in order to realize certain applications. And a number of different desists are known. But desist and implementation of such a generator through hardware logic nay give rise to orthogonality error. To develop Walsh function generator which gets rid of orthogonality error, this paper presents a microprocessor based design and implementation method.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• Nuclear Engineering and Technology
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• v.52 no.4
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• pp.700-707
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• 2020

This study is concerned with the investigation of the half-space albedo problem for "İnönü-linear-quadratic anisotropic scattering" by the usage of Modified FN method. The method is based on Case's method. Therefore, Case's eigenfunctions and its orthogonality properties are derived for anisotropic scattering of interest. Albedo values are calculated for various linear, quadratic and İnönü anisotropic scattering coefficients and tabulated in Tables.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.465-475
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• 2019

Let X be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: ${\varepsilon}$-nonsquareness parameter, $J({\varepsilon},X^*)$; ${\varepsilon}$-boundary parameter, $Q({\varepsilon},X^*)$; the modulus of smoothness, ${\rho}_{X^*}({\varepsilon})$; and ${\varepsilon}$-Pythagorean parameter, $E({\varepsilon},X^*)$, and weak orthogonality parameter, ${\omega}(X)$ in X that imply uniform norm structure in X. Some existing results are extended or approved.

• The Journal of Korea Robotics Society
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• v.10 no.4
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• pp.230-244
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• 2015

Continuous-path motion control such as resolved motion rate control requires online solving of the inverse differential kinematics for a robot. However, the solution space of the inverse differential kinematics related to Jacobian J is not well-established. In this paper, the solution space of inverse differential kinematics is analyzed through categorization of mapping conditions between joint velocities and end-effector velocity of a robot. If end-effector velocity is within the column space of J, the solution or the minimum norm solution is obtained. If it is not within the column space of J, an approximate solution by least-squares is obtained. Moreover, this paper introduces an improved mapping diagram showing orthogonality and mapping clearly between subspaces, and concrete examples numerically showing the concept of several subspaces. Finally, a solver and graphics user interface (GUI) for inverse differential kinematics are developed using MATLAB, and the solution of inverse differential kinematics using the GUI is demonstrated for a vertically articulated robot.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.99-106
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• 2000

A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is Presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and au auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is performed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.10a
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• pp.86-89
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• 2000

In cold forging by multi stage former, crowing process is important process for the high production rate and automation of forging process. But various cropping defects occur in cropping process such as orthogonality, ovality and unevenness, etc. These defects have harmful effects on the dimensional tolerance of products and tool life. So in this study, the cropping experiment is performed to examine influence of cropping process variables(clearance, cutting velocity, H/D) on occurrence of crowing defects and optimum process variables are selected, and then FE analysis is performed to verify influence of these defects on dimensional tolerance and tool life.

• Journal of computational fluids engineering
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• v.5 no.1
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• pp.14-21
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• 2000

A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and an auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is peformed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.