• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.571-580
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• 2013

In this paper, we extend the familiar limit curve theorem in [2] to a situation where each causal curve lies in a sequence of compact interpolating spacetimes converging to a limit Lorentz space in the sense of Lorentzian Gromov-Hausdorff distance.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.277-283
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• 2005

Kriging model is widely used as design analysis and computer experiment (DACE) model in the field of engineering design to accomplish computationally feasible design optimization. In general, kriging model has been applied to many engineering applications as an interpolation model because it is usually constructed from deterministic simulation responses. However, when the responses include not only global nonlinearity but also numerical error, it is not suitable to use Kriging model that can distort global behavior. In this research, generalized kriging model that can represent both interpolation and regression is proposed. The performances of generalized kriging model are compared with those of interpolating kriging model for numerical function with error of normal distribution type and trigonometric function type. As an application of the proposed approach, the response of a simple dynamic model with numerical integration error is predicted based on sampling data. It is verified that the generalized kriging model can predict a noisy response without distortion of its global behavior. In addition, the influences of maximum likelihood estimation to prediction performance are discussed for the dynamic model.

• JSTS:Journal of Semiconductor Technology and Science
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• v.7 no.1
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• pp.28-35
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• 2007

This paper presents a high-speed flash analog-to-digital converter (ADC) for ultra wide band (UWB) receivers. In this flash ADC, the interpolating technique is adopted to reduce the number of the amplifiers and a linear and wide-bandwidth interpolating amplifier is presented. For this ADC, the transistor size for the cascaded stages is inversely scaled to improve the trade-off in bandwidth and power consumption. The active inductor peaking technique is also employed in the pre-amplifiers of comparators and the track-and-hold circuit to enhance the bandwidth. Furthermore, a digital-to-analog converter (DAC) is embedded for the sake of measurements. This chip has been fabricated in $0.13{\mu}m$ 1P8M CMOS process and the total power consumption is 113mW with 1V supply voltage. The ADC achieves 4-bit effective number of bits (ENOB) for input signal of 200MHz at 5-GSample/sec.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.503-510
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• 2004

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;=\;y_i,\;for\;i\;=\;1,\;2,\;\cdots,\;n$. In this paper the following is proved: Let H be a Hilbert space and L be a commutative subspace lattice on H. Let H and y be vectors in H. Let $M_x\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_ix\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;and\;M_y\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_iy\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}. Then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in ${\overline{M_x}}^{\bot}$, AE = EA for all $E\;{\in}\;L\;and\;A^{*}\;=\;A$. (2) $sup\;\{\frac{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;<\;{\infty},\;{\overline{M_u}}\;{\subset}{\overline{M_x}}$ and < Ex, y >=< Ey, x > for all E in L.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.387-395
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• 2004

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{i}\;=\;Y_{i}$, for i = 1,2,...,n. In this article, we showed the following: Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that range(X) is dense in H. Then the following statements are equivalent: (1) There exists an operator A in AlgL such that AX = Y, $A^{*}$ = A and every E in L reduces A. (2) sup ${\frac{$\mid$$\mid${\sum_{i=1}}^n\;E_iYf_i$\mid$$\mid$}{$\mid$$\mid${\sum_{i=1}}^n\;E_iXf_i$\mid$$\mid$}$:n{\epsilon}N,f_i{\epsilon}H\;and\;E_i{\epsilon}L}\;<\;{\infty}$ and = for all E in L and all f, g in H.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.981-986
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• 2011

Given vectors x and y in a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equations $Tx_i=y_i$, for i = 1, 2, ${\cdots}$, n. In this paper the following is proved : Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and y be vectors in $\cal{H}$ and let $P_x$ be the projection onto sp(x). If $P_xE=EP_x$ for each $E{\in}\cal{L}$, then the following are equivalent. (1) There exists an operator A in Alg$\cal{L}$ such that Ax = y, Af = 0 for all f in $sp(x)^{\perp}$ and $A=A^*$. (2) sup $sup\;\{\frac{{\parallel}E^{\perp}y{\parallel}}{{\parallel}E^{\perp}x{\parallel}}\;:\;E\;{\in}\;{\cal{L}}\}$ < ${\infty}$, $y\;{\in}\;sp(x)$ and < x, y >=< y, x >.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.535-539
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• 2007

Given operators X and Y acting on a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX=Y. In this article, we show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $X=(x_{ij})\;and\;Y=(y_{ij})$ be operators in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that AX=Y. (2) There is a bounded sequence $\{\alpha_n\}\;in\;\mathbb{C}$ such that $y_{ij}=\alpha_jx_{ij}\;for\;i,\;j\;{\in}\;\mathbb{N}$. Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax=y. We show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $x=(x_i)\;and\;y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that Ax=y. (2) There is a bounded sequence $\{\alpha_n\}$ in $\mathbb{C}$ such that $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• Spatial Information Research
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• v.19 no.1
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• pp.51-59
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• 2011

We produced true ortho images after interpolating occlusion areas and relief displacement of building as well as producing ortho-images to use backward image of ADS which is a aerial digital camera of line type. Also, I was able to produce high quality ortho-images using a small mount of Ground Control Points(GCP) relatively to compare to frame type camera from the evaluation of horizontal position accuracy using ground check points, photo control points for the verification of ortho-images and true-ortho images. Also, I was able to verify the effectiveness in interpolating occlusion areas cause the length overlap was 100% when producing true-ortho images of line type camera.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.431-436
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;:\;y_i,\;for\;i\;=\;1,\;2,\;{\cdots},\;n$. In this article, we obtained the following : $Let\;x\;=\;\{x_i\}\;and\;y=\{y_\}$ be two vectors in a separable complex Hilbert space H such that $x_i\;\neq\;0$ for all $i\;=\;1,\;2;\cdots$. Let L be a commutative subspace lattice on H. Then the following statements are equivalent. (1) $sup\;\{\frac{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}y\$\mid$}{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}x\$\mid$}\;:\;l\;\in\;\mathbb{N},\;\alpha_{\kappa}\;\in\;\mathbb{C}\;and\;E_{\kappa}\;\in\;L\}\;<\;\infty\;and\;$\mid$y_n\$\mid$x_n$\mid$^{-1}\;=\;1\;for\;all\;n\;=\;1,\;2,\;\cdots$. (2) There exists an operator A in AlgL such that Ax = y, A is a unitary operator and every E in L reduces, A, where AlgL is a tridiagonal algebra.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.517-525
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• 2000

A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given.