• Imaging Science in Dentistry
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• v.40 no.2
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• pp.63-68
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• 2010

Purpose : To compare the CT numbers on 3 cone-beam CT (CBCT) images with those on multi-detector CT (MDCT) image using CT phantom and to develop linear regressive equations using CT numbers to material density for all the CT scanner each. Materials and Methods : Mini CT phantom comprised of five 1 inch thick cylindrical models with 1.125 inches diameter of materials with different densities (polyethylene, polystyrene, plastic water, nylon and acrylic) was used. It was scanned in 3 CBCTs (i-CAT, Alphard VEGA, Implagraphy SC) and 1 MDCT (Somatom Emotion). The images were saved as DICOM format and CT numbers were measured using OnDemand 3D. CT numbers obtained from CBCTs and MDCT images were compared and linear regression analysis was performed for the density, $\rho$ ($g/cm^3$), as the dependent variable in terms of the CT numbers obtained from CBCTs and MDCT images. Results : CT numbers on i-CAT and Implagraphy CBCT images were smaller than those on Somatom Emotion MDCT image (p<0.05). Linear relationship on a range of materials used for this study were $\rho$=0.001H+1.07 with $R^2$ value of 0.999 for Somatom Emotion, $\rho$=0.002H+1.09 with $R^2$ value of 0.991 for Alphard VEGA, $\rho$=0.001H+1.43 with $R^2$ value of 0.980 for i-CAT and $\rho$=0.001H+1.30 with $R^2$ value of 0.975 for Implagraphy. Conclusion: CT numbers on i-CAT and Implagraphy CBCT images were not same as those on Somatom Emotion MDCT image. The linear regressive equations to determine the density from the CT numbers with very high correlation coefficient were obtained on three CBCT and MDCT scan.

• School Mathematics
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• v.10 no.4
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• pp.557-571
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• 2008

The objective of this paper is to study De Morgan's thoughts on teaching and learning negative numbers. We studied De Morgan's point of view on negative numbers, and analyzed his didactical approaches for negative numbers. De Morgan make students explore impossible subtractions, investigate the rule of the impossible subtractions, and construct the signification of the impossible subtractions in succession. In De Morgan' approach, teaching and learning negative numbers are connected with that of linear equations, the signs of impossible subtractions are used, and the concept of negative numbers is developed gradually following the historic genesis of negative numbers. Also, we analyzed the strengths and weaknesses of the De Morgan's approaches compared with the mathematics curriculum.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.51-62
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• 2008

In the 7th-curriculum, only basic arithmetics of complex numbers have been taught. They are taught formally like literal manipulations. This paper analyzes mathematically essential relations between algebra of complex numbers and plane geometry. Historical analysis is also performed to find effective methods of teaching complex numbers in school mathematics. As a result, we can integrates this analysis with school mathematics by help of Viete's operations on right triangles. We conclude that teaching geometric interpretation of complex numbers is possible in school mathematics.

• Korean Journal of Ecology and Environment
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• v.35 no.2 s.98
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• pp.71-78
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• 2002

Seasonal change of total bacterial numbers were estimated in Daechung Reservoir from September, 1998 to August, 1999 and environmental factors which affects total bacterial numbers were estimated. Total bacterial numbers ranged between 1.2 and $19.0{\times}10^6\;cells/ml$ and averaged $6.9{\times}10^6\;cells/ml$. Bacterial numbers changed dynamically with season. The bacterial numbers were highest in July and showed peaks in April and July in sites studied except for the HOE (Hoenam site), In the HOE (Hoenam site), total bacterial numbers increased eve the period of March${\sim}$August. The correlation coefficient between bacterial number and chlorophyll a (<$200\;{\mu}m$) was r = 0.72(p< 0.05) at the MAN (man site). Total bacterial numbers in Daechung Reservoir was diversely changed by the seasonal variation of several environmental quality parameters.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.1-9
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• 2012

The purpose of this paper is to give a new construction of the extended q-Euler numbers and polynomials of higher-order with weight by using p-adic q-integral on $\mathbb{Z}_p$.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.563-579
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• 2010

In this paper we introduce the new analogs of Genocchi numbers and polynomials. Finally, we investigate the zeros of the twisted (h,q)-extension of Genocchi polynomials ${G_{n,q,w}^{(h)}}$(x).

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.657-659
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• 2006

This note gives a counterexample showing that a main theorem of Aytal and Pehliven's (Information Sciences 176 (2006) 734-744) result on statically monotonic and bounded sequences of fuzzy numbers is not valid.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.29-38
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• 2018

In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.99-112
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• 2020

The study is about the bounds of the spectral norms of r-circulant and geometric circulant matrices with the sequences called biperiodic Jacobsthal numbers. Then we give bounds for the spectral norms of Kronecker and Hadamard products of these r-circulant matrices and geometric circulant matrices. The eigenvalues and determinant of r-circulant matrices with the bi-periodic Jacobsthal numbers are obtained.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.125-131
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• 2005

In this paper, we introduce the concept of derivative of the function f : $\mathbb{Q}p{\to} R$ where $\mathbb{Q}p$ is the field of the p-adic numbers and R is the set of real numbers. And some basic theorems on derivatives are given.