• Title/Summary/Keyword: pyramidal number

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A Study on Teaching Material for Enhancing Mathematical Reasoning and Connections - Figurate numbers, Pascal's triangle, Fibonacci sequence - (수학적 추론과 연결성의 교수.학습을 위한 소재 연구 -도형수, 파스칼 삼각형, 피보나치 수열을 중심으로-)

  • Son, Hong-Chan
    • School Mathematics
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    • v.12 no.4
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    • pp.619-638
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    • 2010
  • In this paper, we listed and reviewed some properties on polygonal numbers, pyramidal numbers and Pascal's triangle, and Fibonacci sequence. We discussed that the properties of gnomonic numbers, polygonal numbers and pyramidal numbers are explained integratively by introducing the generalized k-dimensional pyramidal numbers. And we also discussed that the properties of those numbers and relationships among generalized k-dimensional pyramidal numbers, Pascal's triangle and Fibonacci sequence are suitable for teaching and learning of mathematical reasoning and connections.

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The Effects of Sunghyangjunggi-san and Gwackhyangjunggi-san Extracts on Cerebral Ischemia Following the MCA Occlusion in Rat (흰쥐의 중대뇌동맥 결찰로 유발된 뇌허혈에서 성향정기산과 곽향정기산이 신경세포에 미치는 효과)

  • 김선영;이원철
    • The Journal of Korean Medicine
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    • v.22 no.4
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    • pp.142-150
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    • 2001
  • Objectives : The purpose of this investigation is to evaluate and compare the effects of Sunghyangjunggi-san (SH) and Gwackhyangjunggi-san (GH) extracts on reperfusion following the MCA occlusion in rats. Methods : To evaluate the effect of Sunghyangjunggi-san (SH) and Gwackhyangjunggi-san (GH) extracts on reperfusion following the MCA occlusion, the volume of cerebral infarction and edema were measured and the change of the CA1 pyramidal neurons in the hippocampus were investigated by light microscopy. Results : 1. The infarction volume of the control group was 23.6%, that of the GH group was 23.7%, and that of the SH group was 18.5%. 2. The brain edema volume of the control group increased by 16% compared with that of the normal group, that of the GH group increased by 14%, and that of the SH group increased by 9%. 3. The number of surviving pyramidal neurons in the CAI area of the hippocampus was investigated under light microscopy. In the control group, few surviving pyramidal neurons excisted (mean 6.4) and similarly in the GH group (mean 8.5), but in the SH group, the number of surviving pyramidal neurons was significantly higher, to the mean 18.4. Conclusions : According to the above results, in regard to the damage of neurons following cerebral ischemia, the GH group has little effect of the protection of neurons compared to the control group, but the SH group has a remarkable effect.

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Shape optimization for partial double-layer spherical reticulated shells of pyramidal system

  • Wu, J.;Lu, X.Y.;Li, S.C.;Zhang, D.L.;Xu, Z.H.;Li, L.P.;Xue, Y.G.
    • Structural Engineering and Mechanics
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    • v.55 no.3
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    • pp.555-581
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    • 2015
  • Triangular pyramid and Quadrangular pyramid elements for partial double-layer spherical reticulated shells of pyramidal system are investigated in the present study. Macro programs for six typical partial double-layer spherical reticulated shells of pyramidal system are compiled by using the ANSYS Parametric Design Language (APDL). Internal force analysis of six spherical reticulated shells is carried out. Distribution regularity of the stress and displacement are studied. A shape optimization program is proposed by adopting the sequence two-stage algorithm (RDQA) in FORTRAN environment based on the characteristics of partial double-layer spherical reticulated shells of pyramidal system and the ideas of discrete variable optimization design. Shape optimization is achieved by considering the objective function of the minimum total steel consumption, global and locality constraints. The shape optimization of six spherical reticulated shells is calculated with the span of 30m~120m and rise to span ratio of 1/7~1/3. The variations of the total steel consumption along with the span and rise to span ratio are discussed with contrast to the results of shape optimization. The optimal combination of main design parameters for six spherical reticulated shells is investigated, i.e., the number of the optimal grids. The results show that: (1) The Kiewitt and Geodesic partial double-layer spherical reticulated shells of triangular pyramidal system should be preferentially adopted in large and medium-span structures. The range of rise to span ratio is from 1/6 to 1/5. (2) The Ribbed and Schwedler partial double-layer spherical reticulated shells of quadrangular pyramidal system should be preferentially adopted in small-span structures. The rise to span ratio should be 1/4. (3) Grids of the six spherical reticulated shells can be optimized after shape optimization and the total steel consumption is optimized to be the least.

Computer Graphics / Molecular Mechanics Studies of ${\beta}$-Lactam Antibiotics. Geometry Comparison with X-Ray Crystal Structures

  • Chung, Sung-Kee;Chodosh, Daniel F.
    • Bulletin of the Korean Chemical Society
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    • v.10 no.2
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    • pp.185-190
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    • 1989
  • Geometries for a number of representative ${\beta}$ -lactam antibiotics (penams, cephems and monobactams) have been calculated by computer graphics/molecular mechanics energy minimization procedures using both MM2 and AMBER force fields. The calculated geometries have been found in reasonable agreement with the geometries reported in the X-ray crystal structures, especially in terms of the pyramidal character of the amide nitrogen in the ${\beta}$-lactam ring and the Cohen distance. Based on these calculations, it is suggested that the nitrogen atom in the monobactams may also have pyramidal geometries in the biologically active conformations.

CHANGES IN ELECTROPHYSIOLOGICAL PROPERTIES OF NEUROBIOTIN-LABELED PYRAMIDAL CELLS OF HIPPOCAMPUS RECORDED IN VIVO (마취된 흰쥐 해마신경세포에서 Neurobiotin 이온주입으로 인한 신경세포의 생리적 특성의 변화)

  • Lee, Hye-Sook;Lee, Maan-Gee-G.;Kim, Young-Jin;Choi, Byung-Ju
    • Journal of the korean academy of Pediatric Dentistry
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    • v.26 no.2
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    • pp.218-231
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    • 1999
  • Pyramidal cells in the hippocampal CA area were recorded from and filled with neurobiotin in anesthetized rats. The extent of their dendrites and the electropharmacological properties of membrane as well as the effect before and after neurobiotin injection were examined. Pyramidal cells had a high resting membrane potential, a low input resistance, and a large amplitude action potential. A afterhyperpolarization was followed a single action potential. Most pyramidal cells did not display a spontaneous firing. Pyramidal cell displayed weak inward rectification and anodal break excitation in response to negative current injection into the cell. Membrane properties of recorded neurons before and after neurobiotin injection with consecutive current injection were compared. Some properties were significantly increased after labelling(P>0.05); the duration and amplitude of sustained AHP, input resistance, and the number of action potentials for simultaneous intra- and extracellular stimulations. Neurobiotin-filled neurons showed pyramidal morphology. Cells were generally bipolar dendrite processes ramifying in stratum lacunosum-moleculare, radiatum, and oriens.

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Improvement of Surface-enhanced Raman Spectroscopy Response Characteristics of Nanoporous Ag Metal Thin Film with Surface Texture Structures (표면 요철구조를 적용한 나노 다공성 Ag 금속박막의 SERS 응답 특성 개선)

  • Kim, Hyeong Ju;Kim, Bonghwan;Lee, Dongin;Lee, Bong-Hee;Cho, Chanseob
    • Journal of Sensor Science and Technology
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    • v.29 no.4
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    • pp.255-260
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    • 2020
  • In this study, we developed a method of improving the surface-enhanced Raman spectroscopy (SERS) response characteristics by depositing a nanoporous Ag metal thin film through cluster source sputtering after forming a pyramidal texture structure on the Si substrate surface. A reactive ion etching (RIE) system with a metal mesh inside the system was used to form a pyramidal texture structure on the Si surface without following a complicated photolithography process, unlike in case of the conventional RIE system. The size of the texture structure increased with the RIE process time. However, after a process time of 60 min, the size of the structure did not increase but tended to saturate. When the RF power increased from 200 to 250 W, the size of the pyramidal texture structure increased from 0.45 to 0.8 ㎛. The SERS response characteristics were measured by depositing approximately 1.5 ㎛ of nanoporous Ag metal thin film through cluster sputtering on the formed texture structure by varying the RIE process conditions. The Raman signal strength of the nanoporous Ag metal thin film deposited on the Si substrate with the texture structure was higher than that deposited on the general silicon substrate by up to 19%. The Raman response characteristics were influenced by the pyramid size and the number of pyramids per unit area but appeared to be influenced more by the number of pyramids per unit area. Therefore, further studies are required in this regard.

Transmission Electron Microscopy Study of Stacking Fault Pyramids Formed in Multiple Oxygen Implanted Silicon-on-Insulator Material

  • Park, Ju-Cheol;Lee, June-Dong;Krause, Steve J.
    • Applied Microscopy
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    • v.42 no.3
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    • pp.151-157
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    • 2012
  • The microstructure of various shapes of stacking fault pyramids (SFPs) formed in multiple implant/anneal Separation by Implanted Oxygen (SIMOX) material were investigated by plan-view and cross-sectional transmission electron microscopy. In the multiple implant/anneal SIMOX, the defects in the top silicon layer are confined at the interface of the buried oxide layer at a density of ${\sim}10^6\;cm^{-2}$. The dominant defects are perfect and imperfect SFPs. The perfect SFPs were formed by the expansion and interaction of four dissociated dislocations on the {111} pyramidal planes. The imperfect SFPs show various shapes of SFPs, including I-, L-, and Y-shapes. The shape of imperfect SFPs may depend on the number of dissociated dislocations bounded to the top of the pyramid and the interaction of Shockley partial dislocations at each edge of {111} pyramidal planes.

The Effects of Salviae miltiorrhizae Radix, Carthami Flos on Brain Ischemia Experimentally Induced from the Occlusion of Left Common Carotid Artery in Rats (단삼(丹蔘), 홍화(紅花)가 흰쥐의 뇌허혈에 미치는 영향)

  • Kim Bang-Oul;Kim Jeong-Sang;Kim Kyung-Soo;Jeon Sang-Yoon;Hong Seok
    • Herbal Formula Science
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    • v.11 no.2
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    • pp.173-184
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    • 2003
  • Objectives: This study investigates the effects of Salviae miltiorrhizae Radix, Carthami Flos on Brain ischemia of the rats induced from the Occlusion of Lt. Common Carotid Artery. Methods: I observed effects using light microscopes and examined tissue of parietal lobe and hippocampus and VEGF-immunoreactive cells. Results: A small number of VEGF-immunoreactive cells are observed in the control group. VEGF-immunoreactive cells in Salviae miltiorrhizae Radix-administered group were slightly increased compared with control group. VEGF-immunoreactive cells in Carthami Flos-administered group were significantly increased compared with control group. Neurons of parietal lobe and pyramidal cells of hippocampus in the control group were greatly damaged.(neuronal densitity, form of dendrite and axon) On the other hand, neurons of parietal lobe and pyramidal cells of hippocampus in Salviae miltiorrhizae Radix-administered group were less damaged. Neurons of parietal lobe and pyramidal cells of hippocampus in Carthami Flos-administered group were significantly less damaged compared with control group. Conclusion : Salviae miltiorrhizae Radix, Carthami Flos can effect on stimulating angiogenesis and reducinging the damage of neurons in the rats induced from the Occlusion of Lt. Common Carotid Artery.

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A Numerical Study on the Flow and Heat Transfer Characteristics of Aluminum Pyramidal Truss Core Sandwich (알루미늄 피라미드 트러스 심재 샌드위치의 열유동 특성에 관한 수치해석 연구)

  • Kang, Jong-Su;Kim, Sang-Woo;Lim, Jae-Yong
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.3
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    • pp.638-644
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    • 2019
  • In this study, the fluid flow and heat transfer characteristics within sandwich panels are investigated using computational fluid dynamics. Within the sandwich panels having periodic cellular cores, air can freely move inside the core section so that the structure is able to perform multi-functional roles such as simultaneous load bearing and heat dissipation. Thus, there needs to examine the thermal and flow analysis with respect to design variables and various conditions. In this regard, ANSYS Fluent was utilized to explore the flow and heat transfer within the pyramidal truss sandwich structures by varying the truss angle and inlet velocity. Without the entry effect in the first unitcell, the constant rate of pressure and the constant rate of Nusselt number was observed. As a result, it was demonstrated that Nusselt number increases and friction factor decreases as the inlet velocity increases. Moreover, the rate of Nusselt number and friction factor was appreciable in the range of V=1-5m/s due to the transition from laminar to turbulent flow. Regarding the effect of design variable, the variation of truss angle did not significantly influence the characteristics.

The Effects of EGEE on the Morphometry in the Thickness and Histogenesis of Rat Cerebral Cortex During Developmental Phase (발생기 흰쥐 대뇌 피질의 형태 구조에 미치는 Ethylene Glycol Monoethyl Ether의 영향)

  • Lee Eung-Hee;Jeong Gil-Nam;Jo Gi-Jin;Jo Un-Bock
    • Journal of Life Science
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    • v.14 no.6 s.67
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    • pp.975-985
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    • 2004
  • This study attempts to investigate the developmental alterations of rat cerebral cortex, and the effects of EGEE on the developmental cerebral cortex in the prenatal, postnatal and adults were examined by morphological methods and H-E staining was used for the histological changes. In the case of injection of EGEE, at 14 day of fetal phase, parietal cortex was thickest $(95{\pm}12.7\;{\mu}m)$ but, it was thinner than in the control group $(102{\pm}14.0\;{\mu}m)$ and, occipital cortex $(57{\pm}10.5\;{\mu}m)$ compared with other cortexes was the thinnest in fetal phase. In the suckling phase, each cortex grew thick quickly but, after weanning phase, the growth of the cortex slowed and the thickness of cortex was similar to that of cortex in the adult phase. At 105 day after birth, the parietal cortex was thickest $(934{\pm}21.6\;{\mu}m)$ but, decreased compared with control group $(1113{\pm}19.0\;{\mu}m)$. When EGEE was injected in intraperitoneal of rat, the number of neuroblasts per unit area was largest $(207.7{\pm}11.4/10^{-2}\;mm$ at the mantle layer of parietal cortex at 14 day of fetal phase but, decreased compared with control group $(224.2{\pm}13.8/10^{-2}\;mm$ , and the size was largest $(7.5{\pm}1.3\;{\mu}m)$ at the ependymal cell layer of occipital cortex at 3 day after birth but, decreased compared with control group $(9.0{\pm}1.2\;{\mu}m)$. Simillar to control group, the number of granular cells and pyramidal cells were largest at the II and III layer of parietal cortex, but decreased during developmental phase. The size was largest at the IV and V layer of occipital cortex but it was decreased compared with control group. When EGEE was injected in intraperitoneal of rat, the cerebral cortex from fetal phase to 3 day after birth has differentiated into the 3 layers; ependymal, mantle and marginal layer, but empty cisternaes or vacoules in the cerebral cortexes and the condensed phases of neuroblasts were appeared. From 5 day after birth, it has differentiated into the 4 layers; molecular, external granular, mixed layer of internal granular, external and internal pyramidal cells and multiformal layer but, empty cisternaes or vacoules in the granular and pyramidal cell layers were appeared and the number per unit area of neuron was decreased. In the cerebral cortex of the weaning and adult phases, division of cell layers was not clear and empty cisternae was formed in the cortex with the cells in external granular and pyramidal cell layers, was magnified or condensed around blood vessels of neurons.