• Journal for History of Mathematics
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• v.20 no.3
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• pp.59-72
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• 2007

In this paper we find the germ of geometric interpretation of complex number in the Euclid Element and try to show the evolution of geometric interpretation of complex number by through Descarte, Wallis, Vessel. As a result, relations and differences between them are found. They related line with complex number and interpreted complex number geometrically by generalizing the multiplication operation.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.45-59
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• 2011

When using X-12-ARIMA for seasonal adjustment, we usually check whether the series has stable seasonality or not via D8 F-tests, Kruskal-Wallis test, and the spectral diagnostics. In this paper, we develop several smooth tests for seasonality based on a Fourier series to improve the spectral diagnostics of X-12-ARIMA. A simulation study is conducted to compare five smooth tests for seasonality and X-12-ARIMA's D8 F-test an Kruskal-Wallis test. The simulation study shows that smooth tests for seasonality performed well compared with D8 F-tests and a Kruskal-Wallis test.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.701-716
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• 2014

The limiting distribution for the linear placement statistics under the null hypotheses has been provided by Orban and Wolfe [9] and Kim [5] when one of the sample sizes goes to infinity, and by Kim, Lee and Wang [6] when the sample sizes of each group go to infinity simultaneously. In this paper we establish the generalized Kruskal-Wallis one-way analysis of variance for the linear placement statistics.

• Journal of the Korea Society of Computer and Information
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• v.25 no.7
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• pp.175-182
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• 2020

Fisher's classical method for combining independent p-values from continuous distributions is widely used but it is known to be inadequate for combining p-values from discrete probability distributions. Instead, the discrete analog of Fisher's classical method is used as an alternative for combining p-values from discrete distributions. In this paper, firstly we obtain p-values from discrete probability distributions associated with multi-sample location test data (Fisher-Pitman test and Kruskall-Wallis test data) by permutation method, and secondly combine the permutaion p-values by the discrete analog of Fisher's classical method. And we finally compare the combined p-values from both the discrete analog of Fisher's classical method and Fisher's classical method.

• Journal of Environmental Policy
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• v.7 no.3
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• pp.141-160
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• 2008

The effects of disturbance on bird community were studied in Ssanggok Valley and Beopju Temple area, Songni Mt. National Park in $2006{\sim}2008$. We divided three sites by habitat condition such as traffic road(strong disturbance), trail(medium) and control(weak) site. During breeding and non-breeding seasons(n=12), number of species, number of individuals, species diversity and density did not differ among three sites, but in breeding season(n=9), number of species(Kruskal Wallis, $x^2$=10.32, p=0.006), number of individuals(Kruskal Wallis, $x^2$=7.118, p=0.028) and species diversity of birds(Kruskal Wallis, $x^2$=9.847, p=0.007) were significantly higher in trail site with medium disturbance than in other sites. In breeding season, nesting and foraging guild rate were not different among three sites. In guild analysis, hole was the highest nesting guild and canopy was the highest foraging guild in three sites.

• Journal of KIISE:Software and Applications
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• v.41 no.8
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• pp.598-604
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• 2014

In this paper, we develop stepwise regression data envelopment model to select important variables. We formulate null hypothesis to understand the importance of each variable and use Kruskal-Wallis test for this purpose. If the Kruskal-Wallis test does reject the null hypothesis this will imply there is significant fluctuation in the efficiency score relative to base model. And therefore we have to further check the pair of variables that causes the fluctuation in order to determine its importance using Conover-Inman test. The proposed models helps understand the extent of misclassification decision making units as efficient/inefficient when variables are retained or discarded alongside provides useful managerial prescription to make improvement strategies.

• Journal of Sasang Constitutional Medicine
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• v.26 no.1
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• pp.82-97
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• 2014

Objectives The purpose of this study was to survey the Personality and Ordinary Symptoms of Soyangin and to compare the tendency of their personality and symptoms according to Soyangin's major prescription. Methods 331 Soyangin's personality and ordinary symptoms data registered to SCIB(Sasang Constitutional Information Bank) were used. All data were analyzed with Chi square test. Some data were ranked and analyzed with Kruskal-Wallis test and Mann-Whitney test(with Bonferroni correction). Chi square and Kruskal-Wallis test's significant P value was 0.05. Mann-Whitney test's significant P value was 0.005. Results & Conclusions In Chi square test, there is difference in personality and symptoms in Soyangin's major prescription as followed, the degree of masculinity and femininity, the degree of patience, the condition of stool, the degree of appetite, good or bad in digesting, amount of meal, the speed of eating, amount of drinking water, the temperature of drinking water, coldness and hotness in abdomen or not. In Kruskal-Wallis test and Mann-Whitney test, Yanggyuksanhwa-tang is more masculine than Dokhwaljihwang-tang, Hyeongbangsabaek-san, Hyeongbangjihwangtang. Dokhwaljihwang-tang is less appetite than Yanggyuksanhwa-tang and Hyeongbangsabaek-san. Yanggyuksanhwa- tang is more fast in eating than Hyeongbangjihwang-tang.

• Journal for History of Mathematics
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• v.27 no.2
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• pp.127-138
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• 2014

In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

• Journal of Ecology and Environment
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• v.44 no.3
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• pp.196-206
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• 2020

Background: The Himalayan forests are of great importance to sustain the nature and community resource demands. These forests are facing pressures both from anthropogenic activities and ongoing global climatic changes. Poor natural regeneration has been considered a major problem in mountainous forests. To understand the population structure and regeneration status of Larix (Larix griffithiana and Larix himalaica), we conducted systematic vegetation surveys in three high-altitude valleys namely Ghunsa (Kanchenjunga Conservation Area, KCA), Langtang (Langtang National Park, LNP), and Tsum (Manaslu Conservation Area, MCA) in Nepal Himalaya. The average values of diameter at breast height (DBH), height, and sapling height were compared for three sites and two species using Kruskal-Wallis test. Population structure was assessed in terms of proportion of seedlings, saplings, and trees. Regeneration was analyzed using graphical representation of frequencies of seedlings, saplings, and trees in histograms. Results: The results showed that the population structure of Larix in terms of the proportion of seedling, sapling, and tree varied greatly in the three study areas. KCA had the highest record of seedling, sapling, and tree compared to other two sites. Seedlings were the least among three forms and many plots were without seedlings. We found no seedling in MCA study plots. The plot level average DBH variation among sites was significant (Kruskal-Wallis χ² = 7.813, df = 2, p = 0.02) as was between species (Kruskal-Wallis χ² = 5.9829, df = 1, p = 0.014). Similarly, the variation in average tree height was significant (Kruskal-Wallis χ² = 134.23, df = 2, p < 0.001) among sites as well as between species (Kruskal-Wallis χ² = 128.01, df = 1, p < 0.001). All the sites showed reverse J-shaped curve but more pronounced for KCA and MCA. In comparing the two species, Larix griffithiana has clear reverse J-shaped diameter distribution but not Larix himalaica. Conclusion: The varied responses of Larix manifested through regeneration status from spatially distinct areas show that regeneration limitations might be more pronounced in the future. In all the three studied valleys, regeneration of Larix is found to be problematic and specifically for Larix griffithiana in MCA and Larix himalaica in LNP. To address the issues of disturbances, especially serious in LNP, management interventions are recommended to sustain the unique Himalayan endemic conifer.

• Proceedings of the Acoustical Society of Korea Conference
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• 1994.06a
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• pp.818-823
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• 1994