• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.135-141
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• 2013

In this paper we show that a $g$-frame for a Hilbert space $\mathcal{H}$ can be written as a linear combination of two $g$-orthonormal bases for $\mathcal{H}$ if and only if it is a $g$-Riesz basis for $\mathcal{H}$. Also, we show that every $g$-frame for a Hilbert space $\mathcal{H}$ is a multiple of a sum of three $g$-orthonormal bases for $\mathcal{H}$.

• 수산경영론집
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• 제45권2호
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• pp.85-95
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• 2014

Fish stocking is important element of land-based aquaculture management. To maintain constant stocking rate considering biological and economic condition is a convenient strategy in intensive aquaculture. This study is aimed to analyze the effect of over-stocking(more than aquaculture capacity) for certain periods of time. This study make the mathematical decision making model that finds the value of decision variable to minimize cost that sums up the water pool usage cost and sorting cost under critical standing corp constraint. The proposed mathematical decision making model was applied to 12 sample combination of sorting cost and the number of fish on the Oliver flounder culture farms. If a immature fish can be sold for high price than farming cost, restricted over-stocking resulted in a improvement of economic performance. When extensive comparable biological and market data become available, analysis model can be widely applied to yield more accurate results.

• East Asian mathematical journal
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• 제24권3호
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• pp.251-261
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• 2008

Let {${\xi}_j;j\;{\geq}\;1$} be a centered strictly stationary random sequence defined by $S_0\;=\;0$, $S_n\;=\;\Sigma^n_{j=1}\;{\xi}_j$ and $\sigma(n)\;=\;33\sqrt {ES^2_n}$ where $\sigma(t),\;t\;>\;0$, is a nondecreasing continuous regularly varying function. Suppose that there exists $n_0\;{\geq}\;1$ such that, for any $n\;{\geq}\;n_0$ and $0\;{\leq}\;{\varepsilon}\;<\;1$, there exist positive constants $c_1$ and $c_2$ such that $c_1e^{-(1+{\varepsilon})x^2/2}\;{\leq}\;P\{\frac{{\mid}S_n{\mid}}{\sigma(n)}\;{\geq}\;x\}\;{\leq}\;c_2e^{-(1-{\varepsilon})x^2/2$, $x\;{\geq}\;1$ Under some additional conditions, we investigate some limsup results for the increments of partial sum processes of the sequence {${\xi}_j;j\;{\geq}\;1$}.

• 산업공학
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• 제12권1호
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• pp.43-48
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• 1999

This paper indicates deficiencies of existing weighting methods for decision problems that require trading off a selection of one alternative against others. Deficiencies originate from the definition of weight, $W_i$, satisfying that $W_i{\geq}0$ for all i and sums up to one and an assumption of independence between attributes. Thus, existing weighting methods can not handle a situation where all attributes are interrelated, resulting in that attributes can give either positive, or negative, contributions to the value of an alternative. In order to cope with deficiencies, this paper redefines weight and proposes a new causally related weighting method. The proposed method was applied in the study of developing a comprehensive organizational performance measurement system and showed a good performance.

• Structural Engineering and Mechanics
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• 제32권6호
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• pp.725-740
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• 2009

A new simple relation for the estimation of modal correlation coefficients is presented. It is obtained from the decomposition of covariances of modal responses into background and resonant contributions, as it is commonly done for the variances. Thanks to appropriate assumptions, the modal correlation coefficients are estimated as weighted sums of two limit values, corresponding to the background and resonant responses respectively. The weighting coefficients are expressed as functions of the background-to-resonant ratios, which makes the proposed formulation convenient and easily accessible. The simplicity of the mathematical formulation facilitates the physical interpretation. It is for example proved that modal correlation coefficients can be non negligable even in case of well separated natural frequencies, which is sometimes unclear in the litterature. The new relation is mainly efficient in case of large finite element models. It is applied and validated on a finite element buffeting analysis of the Viaduct of Millau, the highest bridge deck ever built so far.

• 호남수학학술지
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• 제30권3호
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• pp.479-486
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• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• Journal of the Optical Society of Korea
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• 제20권6호
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• pp.762-769
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• 2016

The dynamic modulation transfer function (MTF) for image degradation caused by sinusoidal vibration is formulated based on a Bessel function of the first kind. The presented method makes it possible to obtain an analytical MTF expression derived for arbitrary frequency sinusoidal vibration. The error obtained by the use of finite order sum approximations instead of infinite sums is investigated in detail. Dynamic MTF exhibits a stronger random behavior for low frequency vibration than high frequency vibration. The calculated MTFs agree well with the measured MTFs with the slant edge method in imaging experiments. With the proposed formula, allowable amplitudes of any frequency vibration are easily calculated. This is practical for the analysis and design of the line-of-sight stabilization system in the remote sensing camera.

• 한국컴퓨터정보학회지
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• 제15권1호
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• pp.185-190
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• 2007

An image retrieval system is a piece of software that searches identical or similar images based on various image-specific features. This paper proposes a trademark image retrieval system that uses image colors and forms. In the proposed system, input images are segmented into several other regions, and color distribution histograms for different regions are extracted for use as color information. The proposed system uses form information through the preprocessing process such as boundary surface extraction, centroid extraction, angular sampling and, and through calculating the sums of the distances between the centroid and the boundary surfaces, standard deviations, and the ratios between long and short axes. Like this, the color and form information extracted is used to perform retrieval through measuring similarity.

• East Asian mathematical journal
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• 제5권1호
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.