• Journal for History of Mathematics
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• v.28 no.2
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• pp.65-72
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• 2015

The Joseon dynasty (1392-1910) is basically an agricultural country and therefore, the main source of her national revenue is the farmland tax. Thus the farmland tax system becomes the most important state affair. The 4th king Sejong establishes an office for a new law of the tax in 1443 and adopts the farmland tax system in 1444 which is legalized in Gyeongguk Daejeon (1469), the complete code of law of the dynasty. The law was amended in the 19th king Sukjong era. Jo Tae-gu mentioned the new system in his book Juseo Gwan-gyeon (1718) which is also included in Sok Daejeon (1744). Investigating the mathematical structures of the two systems, we show that the systems involve various aspects of mathematics and that the systems are the most precise applications of mathematics in the Joseon dynasty.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.8
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• pp.966-974
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• 2011

The use of ion beams in the micro/nano scale is greatly increased by technology development. Especially, focused ion beams (FIBs) have a great potential to fabricate the device in sub micro scale. Nevertheless, FIB has several limitations, surface swelling in low ion dose regime, precipitation of incident ions, and the redeposition effect due to the sputtered atoms. In this research, we demonstrate a way which can be used to fabricate mold structures on a silicon substrate using FIBs. For the purpose of the demonstration, two essential subjects are necessary. One is that focused ion beam diameter as well as shape has to be measured and verified. The other one is that the accurate rotational symmetric model of ion-solid interaction has to be mathematically developed. We apply those two, measured beam diameter and mathematical model, to fabricate optical lenses mold on silicon. The characteristics of silicon mold fabrication will be discussed as well as simulation results.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.53-58
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• 2003

Many researchers have rigorously studied the nonlinear behavior of stress-strain relationship of concrete using mathematical curves. Most of model equations for stress-strain relationship, however, have been focused on old age concrete, and were not able to adequately represent the behavior of concrete at an early age. A wide understanding on the behavior of concrete from early age to old age is very important in evaluating the durability and service life of concrete structures. In previous study by authors of this paper, a stress-strain model equation for low- and medium-strength concretes was suggested. In this paper, to extend the application region of compressive stress-strain curve to high-strength concrete, an analytical research was performed. An analytical expression of stress-strain curve with strength and age was developed using regression analyses on the experimental results. For the verification of the proposed model equation, it was compared to the experimental data. The result showed that the proposed model equation was not only compatible with the experimental data quite satisfactorily but also describing well the effect of strength and age on stress-strain curve.

• Wind and Structures
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• v.16 no.3
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• pp.279-300
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• 2013

This paper presents a new analysis framework for predicting the internal buffeting forces in bridge components under skew wind. A linear regressive model between the internal buffeting force and deformation under normal wind is derived based on mathematical statistical theory. Applying this regression model under normal wind and the time history of buffeting displacement under skew wind with different yaw angles in wind tunnel tests, internal buffeting forces in bridge components can be obtained directly, without using the complex theory of buffeting analysis under skew wind. A self-anchored suspension bridge with a main span of 260 m and a steel arch bridge with a main span of 450 m are selected as case studies to illustrate the application of this linear regressive framework. The results show that the regressive model between internal buffeting force and displacement may be of high significance and can also be applied in the skew wind case with proper regressands, and the most unfavorable internal buffeting forces often occur under yaw wind.

• Steel and Composite Structures
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• v.22 no.5
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• pp.1193-1214
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• 2016

In this paper, the 3D stress state and inter-laminar stresses in a rotating thin laminated cylinder shell are studied. The thickness of the cylinder is supposed to be thin and it is made of laminated composite material and can have general layer stacking. The governing equations of the cylindrical shell are obtained by employing the Layerwise theory (LWT). The effect of rotation is considered as rotational body force which is induced due to the rotation of the cylinder about its axis. The Layerwise theory (LWT), is used to discrete the partial differential equations of the problem to ordinary ones, in terms of the displacements of the mathematical layers. By applying the Free boundary conditions the solution of the governing equations is completed and the stress state, the inter-laminar stresses, and the edge effect in the rotating cylindrical shells are investigated in the numerical results. To verify the results, LWT solution is compared with the results of the FEM solution and good agreements are achieved. The inter-laminar normal and shear stresses in rotating cylinder are studied and effects of layer stacking and angular velocity is investigated in the numerical results.

• Earthquakes and Structures
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• v.19 no.5
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• pp.315-329
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• 2020

Through bolt connections in Concrete Filled Steel Tubes (CFSTs) has been proved to be good in terms of seismic performance and constructability. Stiffened extended end plate connection with full through type bolt helps to avoid field weld altogether, and hence to improve the quality of joints. An experimental study was conducted on the hysteretic performance of square interior beam-column connections using flat extended end plates with through bolt. The study focuses on the effect of the bond between the tie rod and the core concrete on the cyclic performance of the joint. The study also quantifies how much the interior joint is getting strengthened due to the confinement effect induced by bi-directional bolting, which is widely used in 3D moment resisting frames. For a better understanding of the mechanism and for the prediction of shear capacity of the panel zone, a mathematical model was generated. The various parameters included in the model are the influence of axial load, amount of prestress induced by bolt tightening, anchorage, and the concrete strut action. The study investigates the strength, stiffness, ductility, and energy dissipation characteristics. The results indicate that the seismic resistance is at par with American Institute of Steel Construction (AISC) seismic recommendations. The bidirectional bolting and bond effect have got remarkable influence on the performance of joints.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.273-284
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• 2012

A ring R is called reversibly Armendariz if $b_ja_i=0$ for all $i$, $j$ whenever $f(x)g(x)=0$ for two polynomials $f(x)=\sum_{i=0}^{m}a_ix^i,\;g(x)=\sum_{j=0}^{n}b_jx^j$ over R. It is proved that a ring R is reversibly Armendariz if and only if its polynomial ring is reversibly Armendariz if and only if its Laurent polynomial ring is reversibly Armendariz. Relations between reversibly Armendariz rings and related ring properties are examined in this note, observing the structures of many examples concerned. Various kinds of reversibly Armendariz rings are provided in the process. Especially it is shown to be possible to construct reversibly Armendariz rings from given any Armendariz rings.

• Journal of KIISE:Software and Applications
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• v.26 no.10
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• pp.1167-1167
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• 1999

Although spatial databases support an efficient spatial management on objects in the real world, they have a characteristic that process only spatial information valid at current time, So in case of change in the spatial domain, it is very hard to support an efficient historical management for time-varying spatial information because they delete an old value and then replace with new value that is valid at current time. To solve these problems, there are rapidly increasing of interest for spatiotemporal databases, which serve historical functions for spatial information as well as spatial management functions for an object. However most of them presented in an abstract time-varying spatial phenomenon, but have not presented a concrete policy in spatiotemporal databases. In this paper, we propose a spatiotemporal data model that supports bitemporal time concepts in three dimensional architecture. In the proposed model, not only data types and their operation for object of spatiotemporal databases have been classified, but also mathematical expressions using formal semantics for them have been given. Then, the data structures and their operations based on relational database model as well as object-oriented database model are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.147-152
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• 2006

This paper presents the dynamic characteristics of MR impact damper for vehicle collision system. Various types of mechanism have been proposed for reduce transmitted force to vehicle chassis and finally protect occupants from injury. In the case of frontal collision, the bumper make main role of isolation material for collision attenuation. In this study, proposed bumper system composed of MR impact damper and structures. The MR impact damper is to adopted MR fluid which has reversible properties with applied magnetic field. MR fluid operates under flow mode with Bingham flow and bellows is used for generation of fluid flow. Mathematical model of MR impact damper incorporated with MR fluid is established. Field dependent damping force is investigated with time and frequency domain. The MR impact damper is then incorporated with vehicle crash system. The governing equation of motion of vehicle model is formulated considering occupant model. Dynamic characteristics of vehicle collision system investigated with computer simulation.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.301-310
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• 2015

Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.