• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• Asian-Australasian Journal of Animal Sciences
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• v.19 no.12
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• pp.1702-1705
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• 2006

A simulation study was conducted to evaluate a fine-mapping method exploiting population-wide linkage disequilibrium. Data were simulated according to the pedigree structure based on a large paternal half-sib family population with a total of 1,034 or 2,068 progeny. Twenty autosomes of 100 cM were generated with 5 cM or 1 cM marker intervals for all founder individuals in the pedigree, and marker alleles and a number of quantitative trait loci (QTL) explaining a total of 70% phenotypic variance were generated and randomly assigned across the whole chromosomes, assuming linkage equilibrium between the markers. The founder chromosomes were then descended through the pedigree to the current offspring generation, including recombinants that were generated by recombination between adjacent markers. Power to detect QTL was high for the QTL with at least moderate size, which was more pronounced with larger sample size and denser marker map. However, sample size contributed much more significantly to power to detect QTL than map density to the precise estimate of QTL position. No QTL was detected on the test chromosomes in which QTL was not assigned, which did not allow detection of false positive QTL. For the multiple QTL that were closely located, the estimates of the QTL positions were biased, except when the QTL were located on the right marker positions. Our fine mapping simulation results indicate that construction of dense maps and large sample size is needed to increase power to detect QTL and mapping precision for QTL position.

• Korean Journal of Remote Sensing
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• v.28 no.6
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• pp.635-651
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• 2012

To produce a level-3 monthly composite image from daily level-2 Sea-viewing Wide Field-of-view Sensor (SeaWiFS) chlorophyll-a concentration data set in the East Sea, we applied four average methods such as the simple average method, the geometric mean method, the maximum likelihood average method, and the weighted averaging method. Prior to performing each averaging method, we classified all pixels into normal pixels and abnormal speckles with anomalously high chlorophyll-a concentrations to eliminate speckles from the following procedure for composite methods. As a result, all composite maps did not contain the erratic effect of speckles. The geometric mean method tended to underestimate chlorophyll-a concentration values all the time as compared with other methods. The weighted averaging method was quite similar to the simple average method, however, it had a tendency to be overestimated at high-value range of chlorophyll-a concentration. Maximum likelihood method was almost similar to the simple average method by demonstrating small variance and high correlation (r=0.9962) of the differences between the two. However, it still had the disadvantage that it was very sensitive in the presence of speckles within a bin. The geometric mean was most significantly deviated from the remaining methods regardless of the magnitude of chlorophyll-a concentration values. Its bias error tended to be large when the standard deviation within a bin increased with less uniformity. It was more biased when data uniformity became small. All the methods exhibited large errors as chlorophyll-a concentration values dominantly scatter in terms of time and space. This study emphasizes the importance of the speckle removal process and proper selection of average methods to reduce composite errors for diverse scientific applications of satellite-derived chlorophyll-a concentration data.

• Korean Journal of Remote Sensing
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• v.25 no.4
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• pp.321-338
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• 2009

The objective of this paper is to compare spatial prediction capabilities of univariate kriging algorithms for generating GIS-based thematic maps from ground survey data with asymmetric distributions. Four univariate kriging algorithms including traditional ordinary kriging, three non-linear transform-based kriging algorithms such as log-normal kriging, multi-Gaussian kriging and indicator kriging are applied for spatial interpolation of geochemical As and Pb elements. Cross validation based on a leave-one-out approach is applied and then prediction errors are computed. The impact of the sampling density of the ground survey data on the prediction errors are also investigated. Through the case study, indicator kriging showed the smallest prediction errors and superior prediction capabilities of very low and very high values. Other non-linear transform based kriging algorithms yielded better prediction capabilities than traditional ordinary kriging. Log-normal kriging which has been widely applied, however, produced biased estimation results (overall, overestimation). It is expected that such quantitative comparison results would be effectively used for the selection of an optimal kriging algorithm for spatial interpolation of ground survey data with asymmetric distributions.