• School Mathematics
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• v.8 no.1
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• pp.27-43
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• 2006

The objective of this paper is to design teaching units to foster secondary pre-service teachers' mathematising abilities. In these teaching units we focus on generalizing area of a 2-dimensional triangle and volume of a 3-dimensional tetrahedron to n-volume of n-simplex In this process of generalizing, principle of the permanence of equivalent forms and Cavalieri's principle are applied. To find n-volume of n-simplex, we define n-orthogonal triangular prism, and inquire into n-volume of it. And we find n-volume of n-simplex by using vectors and determinants. Through these teaching units, secondary pre-service teachers can understand and inquire into n-simplex which is generalized from a triangle and a tetrahedron, and n-volume of n-simplex which is generalized from area of a triangle and volume of a tetrahedron. They can also promote natural connection between school mathematics and academic mathematics.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.613-618
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• 1996

In this paper, M will always denote an n- dimensional complete Riemannian manifold and $\omega_n$ is the volume of $S^n$.

• The Journal of the Korean dental association
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• v.11 no.4
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• pp.263-266
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• 1973

The measuring tests on the rest position capacity and the tongue volume were conducted on the one hundred normal dental college students and staffs of Seoul National University in order to study the relationships between the est position Capacity and tongue volume. The results were as follows : 1) The correlation between the rest position capacity and tongue volume was hardly recognized. 2) The correlation between tongue volume and the weight was recognized. 3) Physiologic reflex was coused by the water injected in the mouth in the rest position. 4) Each correlation of the height and cheek thickness to the tongue volume was not recognized.

• The Korean Journal of Ecology
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• v.27 no.1
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• pp.27-33
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• 2004

Cryptomeria japonica plantation was monitored every year during 15 years from 1983 to 1997 for stem diameter and volume. The reciprocal equation, 1/Y = A + B/N, was applied to the relationship between cumulative volume Y and cumulative number N from the largest tree in the stand each year. The parameters A and B, which means respectively the reciprocal of an asymptotic value of total stand stem volume and the reciprocal of the maximum stem volume, are related by a power function. The power functional relationship between A and B derived a linear relationship of B-points ( $N_{B}$, $V_{B}$; $N_{B}$ = B/A, $Y_{B}$ = 1/2A) of each Y-N curve on log-log coordinates. The gradient of B-point line was so steep that the Y-N curve moved parallel upward year by year. The time trajectory of mean stem volume (W) and density ($\rho$) provided evidence in favor of the 3/2 power law of self-thinning, because the gradient of W - $\rho$ trajectory on log-log coordinates approximated to -3/2 at the final stage of stand development. On the basis of the results of Y-N curves and W - $\rho$ trajectory, the time trajectory of maximum stem volume $W_{max obs}$ and $\rho$ was derived theoretically. The gradient of $W_{max obs}$ - $\rho$ trajectory on log-log coordinates is calculated to be -0.6105 at the final stage. The gradient of $W_{max obs}$ - $\rho$ trajectory was steeper than that of W - $\rho$ trajectory at the early stage, while the former is gentler than the latter at the later stage.stage.e.age.e.

• Korean Journal of Computational Design and Engineering
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• v.2 no.1
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• pp.28-34
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• 1997

A swept volume is a useful tool for solving various types of interference problems. Previous works have concentrated on sweeping an object along an arbitrary path, that results in complex algorithms. This paper concerns the volume swept by translating an object along a linear path. After analyzing the structure of the swept volume, we present an incremental algorithm for constructing a swept volume. Our algorithm takes O(n/sup 2/ *.alpha.(n)+T/sub c/) time where n is the number of vertices in the original object and T/sub c/ is time for handling face cycles.

• Imaging Science in Dentistry
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• v.53 no.2
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• pp.91-99
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• 2023

Purpose: This systematic review aimed to investigate the correlation between chronological age and dental pulp volume in cone-beam computed tomography (CBCT). Materials and Methods: The literature was searched in 4 databases(PubMed, Scopus, Web of Science, and Google Scholar). Within each study, the outcome of interest was the correlation (r) between chronological age and pulp volume. A random-effect meta-analysis was conducted. Subgroup analysis was carried out according to sex and tooth type. Results: Of 5,693 identified studies, 27 fulfilled the inclusion criteria and were selected for meta-analysis. These articles focused on single-rooted teeth (n=21), multi-rooted teeth (n=6), maxillary teeth (n=14), mandibular teeth (n=6), and maxillary and mandibular teeth (n=12). The relationship between chronological age and dental pulp volume was examined in the entire population (r= -0.67), men (r= -0.75), and women (r= -0.77) in single- and multi-rooted teeth. The results of the total population analysis showed a relatively strong negative relationship between age and pulp volume. Conclusion: This study suggested that CBCT is a reliable and repeatable tool for dental age estimation. A strong inverse relationship was observed between pulp chamber volume and age. Further studies on the correlation between chronological age and pulp volume of multi-rooted teeth may be beneficial.

• Polymer(Korea)
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• v.26 no.5
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• pp.653-660
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• 2002

The volume phase transition of poly(N-isopropylacrylamide) (PNIPAAm) and poly (N-isopropylacrylamide-co-sodium methacrylate) (P (NIPAAm-co-SMA)) hydrogels crosslinked with poly (ethylene glycol) diacrylate (PEGDA) was investigated in consideration of water content and surface area. The volume phase transition temperature of hydrogel was not affected by the concentration of crosslinking agent, which increased over 40$\^{C}$ by incorporating a small amount of SMA. Higher volume phase transition temperature was obtained when PEGAD was used as a crosslinking agent, suggesting that the chain length of crosslinking agent had a significant effect on the volume phase transition temperature. The surface area of PNIPAAm and P (NIPAAm-co-SMA) gels fell off around the volume phase transition temperature, resulting from the fact that the size of pores reduced remarkably in the course of the volume phase transition. Hence, the surface area and the pore size were considered to be important factors indicating the volume phase transition.

• Journal of Ocean Engineering and Technology
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• v.23 no.3
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• pp.40-45
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• 2009

With the increase in the annealing temperature, the volume fraction of austenite phase increased and the volume fraction of ferrite phase decreased. In compliance with the addition of N, not only the volume fraction of austenite phase was increased but also the austenite structure was made larger. Volume fraction of ${\sigma}$ phase was increased by decreasing of the volume fraction of ferrite phase, with the increase in the aging time and in compliance with the addition of N. As increasing in volume fraction of ${\sigma}$ phase, tensile strength and hardness increased, while elongation and impact value decreased. Elongation slowly decreased and impact value rapidly decreased at the early stage of aging. By the added N, tensile strength, elongation, hardness and impact value was increased.

• Journal of the Korean Chemical Society
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• v.13 no.2
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• pp.121-129
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• 1969

The apparent and partial molal volumes({\phi}\nu$and $V^{\circ}$) of a series of homologous n-alkylamine hydrochlorides $C_nH_{2n+1}NH_3^+Cl^-$, where n varies from zero to four, have been determined by means of a float method at 30$^{\circ}C$ to the fifth decimal place down to 0.01M in aqueous solutions. The experimental results indicate that the partial molal volumes of the salts are almost additive for successive homologues depending on the increment of molecular weight ($CH_2$). It has been observed that the concentration dependence of the ${\Phi}v$ are linear in general and limiting slopes are positive and relatively close to the theoretical values. Anionic partial molal volume of chlorides anion $V^{\circ}_{Cl^-}$ is found to be 18.6 ml $mole^{-1}$, which is in good agreement with the results of other workers. {\phi}\nu$ data also show that in solution the hydrophobic effect of ions are in competition with the charge effect, but the latter, that is, electrostriction seemed to be considerably predominant.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.403-408
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• 2012

In this paper, we prove that if K is a convex body in $E^n$ and $E_i$ and $E_o$ are inscribed ellipsoid and circumscribed ellipsoid of K respectively with ${\alpha}E_i=E_o$, then $\[({\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n{\geq}V(K)V({\Gamma}^{\ast}_pK){\geq}\[(\frac{1}{\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n$. Lutwak and Zhang[6] proved that if K is a convex body, ${\omega}^2_n=V(K)V({\Gamma}_pK)$ if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.