• 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.

• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1197-1222
• /
• 2010

There is a well-known classical reduction formula by Griffiths and Harris for Littlewood-Richardson coefficients, which reduces one part from each partition. In this article, we consider an extension of the reduction formula reducing two parts from each partition. This extension is a special case of the factorization theorem of Littlewood-Richardson coefficients by King, Tollu, and Toumazet (the KTT theorem). This case of the KTT factorization theorem is of particular interest, because, in this case, the KTT theorem is simply a reduction formula reducing two parts from each partition. A bijective proof using tableaux of this reduction formula is given in this paper while the KTT theorem is proved using hives.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2006.03a
• /
• pp.316-323
• /
• 2006

The main objective of this study was to derive a formula of ductility reduction factor, expressed as $R{\mu}$. To attain this objective, a study comprised reduction factors computed for stiffness degrading systems undergoing different levels of ductility and to investigate an accuracy of the formula. Based on this study, the main conclusions can be summarized :(1) The ductility reduction factor is primarily affected by the period of the system and the displacement ductility ratio. (2) The proposed formula is simpler and the inelastic deformations of bridge structures are better than those by the others formulas we used before.

• Journal of Dairy Science and Biotechnology
• /
• v.26 no.1
• /
• pp.27-36
• /
• 2008

This review was written to introduce updated data on the structure and function of the major milk proteins identified as allergens, the characterization of their epitopes in each allergenic milk proteins, and the reduction of milk protein allergenicity. Most mammalian milk protein, even protein present at low concentration, are potential allergens. Epitopes identified in milk proteins are both conformational(structured epitope) and sequential epitopes(linear epitope), throughout the protein molecules. Epitopes on casein and whey proteins are reported to be sequential epitope and conformational epitopes, respectively. Conformational epitopes on whey protein are changed into sequential epitope by heat denaturation during heat treatment. Several methods have been proposed to reduce allergenicity of milk proteins. Most ideal and acceptable method to make hypoallergenic milk or formula, so far, is the hydrolysis of allergenic milk proteins by enzymes that has substrate specificity, such as pepsin, trypsin, or chymotrypsin. Commercial formulas based on milk protein hydrolysate are available for therapeutic purpose, hypoantigenic formula for infants from families with a history of milk allergy and hypoallergenic formula for infants with existing allergic symptoms.

• Journal of Nutrition and Health
• /
• v.38 no.8
• /
• pp.626-636
• /
• 2005

This study was undertaken to examine effects of dietary intake of garcinia cambogia extract, soy peptide and L-carnitine mixture on body weight gain and obesity-related bio-markers in rats fed high-fat diet for 9 weeks with or without regular treadmill exercise. Forty 5-week-old male Sprague-Dawley rats were randomly divided into four groups; sedentary control group (SC), exercised control group (EC), sedentary formula-fed group (SF), and exercised formula-fed group (EF). The SC and EC rats were fed high-fat control diet (fat comprises$40\%$ of total caloris), and SF and EF rats were fed high-fat formula (composed of garcinia cambogia, soy peptide and L-carnitine) supplemented diet. Statistical analyses by two-way ANOVA indicated that the regular treadmill exercise significantly lowered cumulative body weight gain, total visceral fat mass, and epididymal, perirenal and retroperitoneal fat pad weights, and serum concentrations of total cholesterol and LDL + VLDL cholesterol, insulin, c-peptide and leptin. Feeding the formula also resulted in significant reductions in cumulative body weight gain and visceral fat pad weights, along with other related parameters including serum total and LDL + VLDL cholesterol levels, and hepatic enzyme activities involved in fatty acid synthesis. Statistical analyses by one-way ANOVA revealed that the formula consumption significantly improved body weight gain ($18\%$ reduction), total visceral fat weight ($20\%$ reductions), and serum total ($43\%$ reduction) and LDL + VLDL cholesterol ($54\%$ reduction) levels, as well as serum levels of insulin ($49\%$ reduction), and c-peptide ($41\%$ reduction) in sedentary rats, but failed to exhibit significant reductions in these indices in animals under treadmill exercise program. Taken together, these results suggest that the treadmill exercise per n exhibited significant improvements in body fat reduction and other related bio-markers, and so the formula consumption did not achieve a further significant reductions in these bio-markers in exercised rats. Nevertheless, animals fed the formula with regular exercise showed the most efficient weight reduction compared to other groups either fed formula without exercise or received regular exercise without dietary supplementation.

• 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 Industrial Technology
• /
• v.26 no.A
• /
• pp.153-161
• /
• 2006

The main objective of this study was to derive a formula of ductility reduction factor, expressed as $R_{\mu}$. To attain this objective, a study comprised reduction factors computed for stiffness degrading systems undergoing different levels of ductility and to investigate an accuracy of the formula. Based on this study, the main conclusions can be summarized :(1) The ductility reduction factor is primarily affected by the period of the system and the displacement ductility ratio. (2) The proposed formula is simpler and the inelastic deformations of bridge structures are better than those by the others formulas we used before.

• Kyungpook Mathematical Journal
• /
• v.55 no.2
• /
• pp.439-447
• /
• 2015

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.

• Earthquakes and Structures
• /
• v.6 no.3
• /
• pp.301-316
• /
• 2014

This paper is devoted to investigate the effects of SSI on strength reduction factor of multistory buildings. A new formula is proposed to estimate strength reduction factors for MDOF structure-soil systems. It is concluded that SSI reduces the strength reduction factor of MDOF systems. The amount of this reduction is relevant to the fundamental period of structure, soil flexibility, aspect ratio and ductility of structure, and could be significantly different from corresponding fixed-base value. Using this formula, measuring the amount of this error could be done with acceptable accuracy. For some practical cases, the error attains up to 50%.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.22 no.3
• /
• pp.149-155
• /
• 2010

The existing formula for estimating the wave overtopping are mainly about the perpendicularly incident wave to the structure and wave overtopping formula for the obliquely incident wave are rare. Moreover, these formula present only the overtopping reduction factor(${\gamma}_{\beta}$) with respect to the incident wave angle rather than the spatial distribution of overtopping along the structures because the length of model is relatively too short for the wave to propagate along the structure. In this study, the wave overtopping reduction factor considering the spatial variation of wave overtopping along the vertical wall is investigated using the hydraulic model tests and the results are compared with the those of EurOtop(2007). The wave overtopping reduction factor is modified for ${\beta}$ > $45^{\circ}$ condition.