• 대한수학회보
• /
• 제45권3호
• /
• 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.

• 대한수학회지
• /
• 제47권6호
• /
• 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.

• 한국지진공학회:학술대회논문집
• /
• 한국지진공학회 2006년도 학술발표회 논문집
• /
• 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
• /
• 제26권1호
• /
• 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
• /
• 제38권8호
• /
• 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.

• 호남수학학술지
• /
• 제32권2호
• /
• 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.

• 산업기술연구
• /
• 제26권A호
• /
• 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
• /
• 제55권2호
• /
• 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
• /
• 제6권3호
• /
• 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%.

• 한국해안·해양공학회논문집
• /
• 제22권3호
• /
• pp.149-155
• /
• 2010

기존 월파량 산정식의 대부분은 파랑이 구조물에 직각으로 입사하는 조건에 대한 산정식으로서 경사입사파에 대한 연구는 미미한 실정이다. 또한 경사입사파 조건의 경우에도 상대적으로 짧은 모형을 실험에 적용함에 따라 경사입사파 내습시 구조물을 따라서 진행하는 파랑에 의한 월파를 고려할 수 없었으며, 단지 입사각에 따른 월파량 저감효과를 고려할 수 있는 월파량 저감계수(${\gamma}_{\beta}$)를 도입한 월파량 산정식을 제시하였다. 본 연구에서는 경사입사파 내습시 구조물 전면을 따라 진행하는 파에 의한 월파, 즉 월파의 공간적인 분포를 고려한 월파량 저감계수를 평면 수리실험을 통하여 제시하였다. 산정된 월파량 저감계수는 EurOtop(2007)에서 제시된 결과와 비교하였으며, 입사각이 $45^{\circ}$ 이상인 조건에 대해 EurOtop(2007)에서 제시한 월파량 저감계수를 개선하였다.