• Bulletin of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.485-494
• /
• 2008

There are two well known reduction formulae for structural constants of the cohomology ring of Grassmannians, i.e., Littlewood-Richardson coefficients. Two reduction formulae are a conjugate pair in the sense that indexing partitions of one formula are conjugate to those of the other formula. A nice bijective proof of the first reduction formula is given in the authors' previous paper while a (combinatorial) proof for the second reduction formula in the paper depends on the identity between Littlewood-Richardson coefficients of conjugate shape. In this article, a direct bijective proof for the second reduction formula for Littlewood-Richardson coefficients is given. Our proof is independent of any previously known results (or bijections) on tableaux theory and supplements the arguments on bijective proofs of reduction formulae in the authors' previous paper.

• Honam Mathematical Journal
• /
• v.32 no.2
• /
• pp.271-281
• /
• 2010

Inspired by the reduction formulae between intersection numbers on Grassmannians obtained by Griffiths-Harris and the factorization theorem of Littlewood-Richardson coefficients by King, Tollu and Toumazet, eight reduction formulae has been discovered by the author and others. In this paper, we prove r = 1 reduction formula by constructing a bijective map between suitable sets of Littlewood-Richardson tableaux.

• Journal of the Korean Institute of Navigation
• /
• v.9 no.2
• /
• pp.1-12
• /
• 1985

In order to computerize the sight reduction process completely, the coordinates of celestial bodies have to be calculated. The author calculates the equtorial coordinates of the sun and stars using formulae by computer programming. And they are compared with data from an nautical almanac. Generally, data based on formulae is slightly less accurate than those derived from an nautical almanac. In the case of calculating coordinates of the sun, maximum error of GHA is $0{'\\.}2$, and that of declination is $0{'\\.}1$.

• Smart Structures and Systems
• /
• v.26 no.4
• /
• pp.481-493
• /
• 2020

The negative stiffness spring and inerter are both characterized by the negative stiffness effect in the force-displacement relationship, potentially yielding an amplifying mechanism for dashpot deformation by being incorporated with a series tuning spring. However, resisting forces of the two mechanical elements are dominant in different frequency domains, thus leading to necessary complementarity in terms of vibration control and the amplifying benefit. Inspired by this, this study proposes a Negative Stiffness Inerter System (NSIS) as an earthquake protection system and developed analytical design formulae by fully utilizing its advantageous features. The NSIS is composed of a sub-configuration of a negative stiffness spring and an inerter in parallel, connected to a tuning spring in series. First, closed-form displacement responses are derived for the NSIS structure, and a stability analysis is conducted to limit the feasible domains of NSIS parameters. Then, the dual advantageous features of displacement reduction and the dashpot deformation amplification effect are revealed and clarified in a parametric analysis, stimulating the establishment of a displacement-based optimal design framework, correspondingly yielding the design formulae in analytical form. Finally, a series of examples are illustrated to validate the derived formulae. In this study, it is confirmed that the synergistic incorporation of the negative stiffness spring and the inerter has significant energy dissipation efficiency in a wide frequency band and an enhanced control effect in terms of the displacement and shear force responses. The developed displacement-based design strategy is suitable to utilize the dual benefits of the NSIS, which can be accurately implemented by the analytical design formulae to satisfy the target vibration control with increased energy dissipation efficiency.

• Kyungpook Mathematical Journal
• /
• v.20 no.2
• /
• pp.251-259
• /
• 1980

• Structural Engineering and Mechanics
• /
• v.62 no.4
• /
• pp.443-453
• /
• 2017

The performance of bolted side-plated (BSP) beams is affected by the degree of transverse partial interaction, which is a result of the interfacial slip caused by transverse shear transfer between the bolted steel plates and the reinforced concrete beams. However, explicit formulae for the transverse shear transfer profile have yet to be derived. In this paper, a simplified piecewise linear shear transfer model was proposed based on force superposition principle and simplification of shear transfer profiles derived from a previous numerical study. The magnitude of shear transfer was determined by force equilibrium and displacement compatibility condition. A set of design formulae for BSP beams under several basic load cases was also derived. Then the model was verified by test results. A worked example was also provided to illustrate the application of the proposed design formulae. This paper sheds some light on the shear force transfer mechanism of anchor bolts in BSP beams, and offers a practical method to evaluate the influence of transverse partial interaction in strengthening design.

• Journal of the Korean Geotechnical Society
• /
• v.15 no.1
• /
• pp.5-13
• /
• 1999

Maximum stress in pile is developed when it is driven. If the stress is greater than allowable stress of the pile, the pile will be damaged and result in stability problem. Therefore, the stress should be estimated correctly beforehand and overstress should be prevented during pile driving. There are many methods to estimate compressive stresses in concrete piles when they are driven. Nowadays, computer analysis on wave equation offers a satisfactory results. But. under certain circumstances, application of this method is difficult. Then, estimation of the stress utilizing simple formulae might be practical. In this study, relatively reasonable formulae were selected and the stresses which were measured in situ and calculated from the formulae were compared and analysed. The results show that the calculated values from Uto and Huyuki's formula were reasonably accurate and more accurate values were acquired if the values are modified by multiplying the reduction factors according to ground and construction conditions.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10a
• /
• pp.1018-1023
• /
• 1992

In this paper we proposed the systematic method of reducing the order of controller with robustness. State space formulae for all controllers is found by solving two coupled J-lossless coprime factorizations and model reduction problem. To reduce the order of controller, balanced truncation and Hankel approximation are used.

• Herbal Formula Science
• /
• v.17 no.1
• /
• pp.163-173
• /
• 2009

Objectives : The goal of this study was to investigative the effect of Gardeniae Fructus (GF)as antidepressant in the forced swimming test(FST) model rats. Methods : The expressions of corticotropin-releasing factor(CRF), tyrosine hydroxylase (TH) and c-fos were measured by immunohistochemical method at paraventricular nucleus(PVN), locus coeruleus (LC) and ventral tegmental area(VTA). Results : The duration of immobility in FST was significantly decreased in the GF 100mg/kg groups (p<0.05). CRF expression was significantly decreased at PVN in the GF 100 mg/kg and 400mg/kg treated group in comparison with the control group, respectively (p<0.01). c-fos expression was decreased at PVN in the GF 100 mg/kg treated group with no significance. TH expression was significantly decreased in the GF 100 mg/kg and 400mg/kg treated group in comparison with the control group, at LC and VTA respectively (p<0.001). Conclusion : According to the results, it can be considered that Gardeniae Fructus has antidepressant effect by showing the reduction of immobility in FST through the reduction of CRF, TH expression.

• Herbal Formula Science
• /
• v.17 no.1
• /
• pp.129-140
• /
• 2009

Objectives : The goal of this study was to investigate the effect of Moutan Cortex as antidepressant in forced swimming test(FST) model. Methods : The expressions of corticotropin-releasing Factor(CRF), c-Fos and tyrosine hydroxylase(TH) were measured with immunohistochemical method at paraventricular nucleus (PVN), locus coeruleus(LC) and ventral tegmental area(VTA). Results : The duration of immobility in the forced swimming test was significantly decreased in the Moutan Cortex 100 mg/kg treated group in comparison with the control group(p<0.01). CRF and c-Fos expressions at PVN were decreased in the Moutan Cortex 100mg/kg treated group in comparison with the control group. But only the expression of c-Fos was shown the significance(p<0.05). TH expressions at LC and VTA were significantly decreased in the Moutan Cortex 100mg/kg and 400mg/kg treated group in comparison with the control group(p<0.001). Conclusion : According to the results, Moutan Cortex has the antidepressant effect by showing the reduced immobility through the reduction of c-Fos expression at PVN and the reduction of TH expression at LC and VTA.