• Journal for History of Mathematics
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• v.20 no.3
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• pp.1-16
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• 2007

In order to generalize theory of series in Iksan(翼算), we introduce a concept of double sequence of partial sums and elementary double sequence of partial sums, which play a dominant role in the study of double sequences of partial sums. We introduce a concept of finitely generated double sequence of partial sums and find a necessary and sufficient condition for those double sequences. Finally we prove a multiplication theorem for tetrahedral numbers and for 4 dimensional tetrahedral numbers.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1173-1246
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• 2019

We find all P-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces (a corrected version of) Jan Steven's list [Manuscripta Math. 1993] of the numbers of P-resolutions of each singularities. We then compute the dimensions and Milnor numbers of the corresponding irreducible components of the reduced base spaces of versal deformations of each singularities. Furthermore we realize Milnor fibers as complements of certain divisors (depending only on the singularities) in rational surfaces via the semi-stable minimal model program for 3-folds. Then we compare Milnor fibers with minimal symplectic fillings, where the latter are classified by Bhupal and Ono [Nagoya Math. J. 2012]. As an application, we show that there are 6 pairs of entries in the list of Bhupal and Ono [Nagoya Math. J. 2012] such that two entries in each pairs represent diffeomorphic minimal symplectic fillings.

• Korean Journal of Computational Design and Engineering
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• v.12 no.4
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• pp.255-262
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• 2007

In the finite element analysis of forming process, objects are described with a finite number of elements and nodes and the approximated solutions can be obtained by the variational principle. One of the shortcomings of a finite element analysis is that the structure of mesh has become inefficient and unusable because discretization error increases as deformation proceeds due to severe distortion of elements. If the state of current mesh satisfies a certain remeshing criterion, analysis is stopped instantly and resumed with a reconstructed mesh. In the study, a new remeshing algorithm using tetrahedral elements has been developed, which is adapted to the desired mesh density. In order to reduce the discretization error, desired mesh sizes in each lesion of the workpiece are calculated using the Zinkiewicz and Zhu's a-posteriori error estimation scheme. The pre-constructed mesh is constructed based on the modified point insertion technique which is adapted to the density function. The object domain is divided into uniformly-sized sub-domains and the numbers of nodes in each sub-domain are redistributed, respectively. After finishing the redistribution process of nodes, a tetrahedral mesh is reconstructed with the redistributed nodes, which is adapted to the density map and resulting in good mesh quality. A goodness and adaptability of the constructed mesh is verified with a testing measure. The proposed remeshing technique is applied to the finite element analyses of forging processes.

• The Journal of the Acoustical Society of Korea
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• v.43 no.1
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• pp.72-77
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• 2024

Recently, the necessity for sound source localization has grown significantly across various industrial sectors. Among the sound source localization methods, sound intensimetry has the advantage of having high accuracy even with a small microphone array. However, the increase in localization error at high Helmholtz numbers have been pointed out as a limitation of this method. The study proposes a method to compensate for the bias error of the measured sound intensity vector according to the Helmholtz numbers by applying deep learning. The method makes it possible to estimate the accurate direction of arrival of the source by applying a dense layer-based deep learning model that derives compensated sound intensity vectors when inputting the sound intensity vectors measured by a tetrahedral microphone array for the Helmholtz numbers. The model is verified based on simulation data for all sound source directions with 0.1 < kd < 3.0. One can find that the deep learning-based approach expands the measurement frequency range when implementing the sound intensimetry-based sound source localization method, also one can make it applicable to various microphone array sizes.

• The Journal of Advanced Prosthodontics
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• v.12 no.2
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• pp.67-74
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• 2020

PURPOSE. This study evaluated the influence of prosthesis weight and number of implants on the bone tissue microstrain. MATERIALS AND METHODS. Fifteen (15) fixed full-arch implant-supported prosthesis designs were created using a modeling software with different numbers of implants (4, 6, or 8) and prosthesis weights (10, 15, 20, 40, or 60 g). Each solid was imported to the computer aided engineering software and tetrahedral elements formed the mesh. The material properties were assigned to each solid with isotropic and homogeneous behavior. The friction coefficient was set as 0.3 between all the metallic interfaces, 0.65 for the cortical bone-implant interface, and 0.77 for the cancellous bone-implant interface. The standard earth gravity was defined along the Z-axis and the bone was fixed. The resulting equivalent strain was assumed as failure criteria. RESULTS. The prosthesis weight was related to the bone strain. The more implants installed, the less the amount of strain generated in the bone. The most critical situation was the use of a 60 g prosthesis supported by 4 implants with the largest calculated magnitude of 39.9 mm/mm, thereby suggesting that there was no group able to induce bone remodeling simply due to the prosthesis weight. CONCLUSION. Heavier prostheses under the effect of gravity force are related to more strain being generated around the implants. Installing more implants to support the prosthesis enables attenuating the effects observed in the bone. The simulated prostheses were not able to generate harmful values of peri-implant bone strain.

• Geomechanics and Engineering
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• v.28 no.5
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• pp.521-529
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• 2022

This research work deals with the development of air pluviation method for preparing uniform sand specimens for conducting large scale laboratory testing. Simulating real field conditions and to get reliable results, air pluviation method is highly desirable. This paper presents a special technique called air pluviation or sand raining technique for achieving uniform relative density. The apparatus is accompanied by a hopper, shutters with different orifice sizes and numbers and set of sieves. Before using this apparatus, calibration curves are drawn for relative density against different height of fall (H) and shutter sizes. From these calibration curves, corresponding to the desired relative density of 60%, the shutter size of 13mm and height of fall of 457.2 mm, are selected and maintained throughout the pluviation process. The density obtained from the mobile pluviator is then verified using the Dynamic Cone Penetrometer (DCP) test where the soil is poured in the box using defined shutter size and fall height. The results obtained from the DCP test are averaged as 60±0.5 which was desirable. The mobile pluviator used in this research is also capable of obtaining relative densities up to 90%. The instrument is validated using experimental and numerical approach. In numerical study, Plaxis 3D software is used in which the soil mass is defined by 10-Node tetrahedral elements and 6-Node plate is used to simulate plate behavior in the validation phase. The results obtained from numerical approach were compared with that of experimental one which showed very close correlation.

• Journal of the Korean Chemical Society
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• v.40 no.7
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• pp.474-482
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• 1996

Two crystal structures of the vacuum dehydrated $Ag^+$-exchanged zeolite X have been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd3 at 21(1)$^{\circ}C$ (a=24.922(1)${\AA}$ and a=24.901(1)${\AA}$, respectively). Each crystal was ion exchanged in flowing streams of aqueous $AgNO_3$ for three days. The first crystal was dehydrated at 300$^{\circ}C$ and $2{\times}10^{-6$torr for two days. The second crystal was similarly dehydrated at 350$^{\circ}C$. Their structures were refined to the final error indices, $R_1=0.095\;and\;R_2=0.092$ with 227 reflections, and $R_1=0.096\;and\;R_2=0.087$ with 334 reflections, respectively, for which I > 3${\sigma}$(I). In the first crystal, Ag species are found at five different crystallographic sites: sixteen $Ag^+$ ions fill the site I, the center of the double 6-ring, thirty-two Ag0 atoms fill the I' site in the sodalite cavities opposite double six-rings, seventeen $Ag^+$ ions lie at the 32-fold site II' inside the sodalite cavity at the single six-oxygen ring in the supercage, fifteen Ag+ ions lie at the 32-fold site II, in the supercage, and the remaining twelve $Ag^+$ ions lie at site III' in the supercage at a little off two-fold axes. In the second crystal, all Ag species are located similarly as crystal 1; 16 at site I, 28 at site I', 16 at site II, 16 at site II', 6 at site III and 6 at site III'. Total 88 silver species were found per unit cell. The remaining four Ag atoms were migrated out of the zeolite framework to form small silver crystallites on the surface of the zeolite single crystal. In the first structure, the numbers of Ag atoms per unit cell are approximately 32.0 and these may form tetrahedral $Ag_4$ clusters at the centers of the sodalite cavities. The probable four-atom cluster is stabilized by coordination to two $Ag^+$ ions. The Ag-Ag distance in the cluster, ca. 3.05 ${\AA}$, is a little longer than 2.89 ${\AA}$, Ag-Ag distance in silver metal. At least two six-ring $Ag^+$ ions on sodalite cavity (site II') must necessarily approach this cluster and this cluster may be viewed as a distorted octahedral silver cluster, (Ag6)2+.