• Journal of Information Processing Systems
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• v.13 no.2
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• pp.305-320
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• 2017

The selection of subset size is of great importance to the accuracy of digital image correlation (DIC). In the traditional DIC, a constant subset size is used for computing the entire image, which overlooks the differences among local speckle patterns of the image. Besides, it is very laborious to find the optimal global subset size of a speckle image. In this paper, a self-adaptive and bidirectional dynamic subset selection (SBDSS) algorithm is proposed to make the subset sizes vary according to their local speckle patterns, which ensures that every subset size is suitable and optimal. The sum of subset intensity variation (${\eta}$) is defined as the assessment criterion to quantify the subset information. Both the threshold and initial guess of subset size in the SBDSS algorithm are self-adaptive to different images. To analyze the performance of the proposed algorithm, both numerical and laboratory experiments were performed. In the numerical experiments, images with different speckle distribution, different deformation and noise were calculated by both the traditional DIC and the proposed algorithm. The results demonstrate that the proposed algorithm achieves higher accuracy than the traditional DIC. Laboratory experiments performed on a substrate also demonstrate that the proposed algorithm is effective in selecting appropriate subset size for each point.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.215-220
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• 2002

Since P. Erdos introduced the concept of "subset-sum-distinctness", lots of mathematicians have been interested in a "dense" set having distinct subset sums. In this paper, we establish a couple of theorems on maximal subset-sun-distinct sequence with respect to the set inclusion.

• Journal of the Optical Society of Korea
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• v.16 no.4
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• pp.372-380
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• 2012

The optical method Digital Speckle Correlation Measurement (DSCM) has been extensively applied due its capability to measure the entire displacement field over a body surface. A formula of displacement measurement errors by the gradient-based DSCM method was derived. The errors were found to explicitly relate to the image grayscale errors consisting of sub-pixel interpolation algorithm errors, image noise, and subset deformation mismatch at each point of the subset. A power-law dependence of the standard deviation of displacement measurement errors on the subset size was established when the subset deformation was rigid body translation and random image noise was dominant and it was confirmed by both the numerical and experimental results. In a gradient-based algorithm the basic assumption is rigid body translation of the interrogated subsets, however, this is in contradiction to the real circumstances where strains exist. Numerical and experimental results also indicated that, subset shape function mismatch was dominant when the order of the assumed subset shape function was lower than that of the actual subset deformation field and the power-law dependence clearly broke down. The power-law relationship further leads to a simple criterion for choosing a suitable subset size, image quality, sub-pixel algorithm, and subset shape function for DSCM.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.757-768
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• 2003

In 1967, as an answer to the question of P. Erdos on a set of integers having distinct subset sums, J. Conway and R. Guy constructed an interesting sequence of sets of integers. They conjectured that these sets have distinct subset sums and that they are close to the best possible with respect to the largest element. About 30 years later (in 1996), T. Bohman could prove that sets from the Conway-Guy sequence actually have distinct subset sums. In this paper, we generalize the concept of subset-sum-distinctness to k-SSD, the k-fold version. The classical subset-sum-distinct sets would be 1-SSD in our definition. We prove that similarly derived sequences as the Conway-Guy sequence are k-SSD.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.521-531
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• 2002

Various diagnostic techniques for identifying influential observations are mostly based on the deletion of a single observation. While such techniques can satisfactorily identify influential observations in many cases, they will not always be successful because of some mask effect. It is necessary, therefore, to develop techniques that examine the potentially influential effects of a subset of observations. The partial regression plots can be used to examine an influential observation for a single parameter in multiple linear regression. However, it is often desirable to detect influential observations for a subset of regression parameters when interest centers on a selected subset of independent variables. Thus, we propose a diagnostic measure which deals with detecting influential observations on a subset of regression parameters. In this paper, we propose a measure M, which can be effectively used for the detection of influential observations on a subset of regression parameters in multiple linear regression. An illustrated example is given to show how we can use the new measure M to identify influential observations on a subset of regression parameters.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.33-41
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• 2020

We introduced the concept of the 𝜖₀-density and the 𝜖₀-dense ace in [1]. This concept is related to the structure of employment. In addition to the double capacity theorem which was introduced in [1], we need the minimal dense subset. In this paper, we investigate a concept of the minimal 𝜖₀-dense subset in the Euclidean m dimensional space.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.223-230
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• 2008

In this paper, we present an upper bound of the reciprocal sums of generalized subset-sum-distinct sequences with respect to the first terms of the sequences. And we show the suggested upper bound is best possible. This is a kind of generalization of [1] which contains similar result for classical subset-sum-distinct sequences.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.913-919
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• 2014

We investigate the relationships between the space X and the hyperspaces concerning admissibility and connectedness im kleinen. The following results are obtained: Let X be a Hausdorff continuum, and let A, $B{\in}C(X)$ with $A{\subset}B$. (1) If X is c.i.k. at A, then X is c.i.k. at B if and only if B is admissible. (2) If A is admissible and C(X) is c.i.k. at A, then for each open set U containing A there is a continuum K and a neighborhood V of A such that $V{\subset}IntK{\subset}K{\subset}U$. (3) If for each open subset U of X containing A, there is a continuum B in C(X) such that $A{\subset}B{\subset}U$ and X is c.i.k. at B, then X is c.i.k. at A. (4) If X is not c.i.k. at a point x of X, then there is an open set U containing x and there is a sequence $\{S_i\}^{\infty}_{i=1}$ of components of $\bar{U}$ such that $S_i{\longrightarrow}S$ where S is a nondegenerate continuum containing the point x and $S_i{\cap}S={\emptyset}$ for each i = 1, 2, ${\cdots}$.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.573-585
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• 2020

We introduced the concepts of the generalized accumulation points and the generalized density of a subset of the Euclidean space in [1] and [2]. Using those concepts, we introduce the concepts of the generalized closure, the generalized interior, the generalized exterior and the generalized boundary of a subset and investigate some properties of these sets. The generalized boundary of a subset is closely related to the classical boundary. Finally, we also introduce and study a concept of the thickness of a subset.