• Title/Summary/Keyword: Triple Product

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The Relationship between Kinematics of the Limb motions and Changes in the Velocity of the Center of Gravity of the Whole Body during Support Phase in the Triple Jump (세단뛰기 지지국면 시 사지의 운동학적 변인과 전신 무게중심의 속도 변화와의 관계)

  • Ryu, Jae-Kyun;Jung, Chul-Jung;Park, Jin
    • Korean Journal of Applied Biomechanics
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    • v.13 no.3
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    • pp.27-46
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    • 2003
  • The purposes of this study were to determine the functions of actions of the limbs during each of the three support phases of the triple jump and their relationships with the performance of the triple jump. Four elite male triple jumpers were participated as subjects. The statistical analyses used were the Pearson product moment correlation coefficient for establishing relationships and simple regression analyses to determine and compare the relationships between the change of the horizontal velocity and the change of the vertical velocity during different support phases. A level of significance at p<.05 was set. The actions of the arms were responsible for about 25%, 25%, and 30% of the decrease in the horizontal velocity of the whole body center of gravity during the support phases of the hop, step, and jump, respectively. The change in the velocities of the whole body center of gravity due to the actions of the free limbs were significantly related with the whole body center of gravity during each support phase. The action of the support leg was associated with the decrease in the horizontal velocity and the increase in the vertical velocity of the whole body center of gravity during each support phase.

The Relationship between the Angular Momentum of the Limbs and the Performance during Support Phase of the Triple Jump (세단뛰기 지지국면 시 사지의 각운동량과 운동수행과의 관계)

  • Ryu, Jae-Kyun;Yeo, Hong-Chul
    • Korean Journal of Applied Biomechanics
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    • v.14 no.1
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    • pp.65-81
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    • 2004
  • The purposes of this study were to determine the functions of actions of the limbs during each of the three support phases of the triple jump and their relationships with the performance of the triple jump. Four elite male triple jumpers were participated as subjects. The Pearson product moment correlation coefficient were used to determine and compare the relationships between the change in each component of the normalized angular momentum of the whole body about center of gravity and the actions of the extremities during different support phases. A level of significance at $\alpha$=.05 was set. After analyzing the angular momentum and correlation during support phase of the hop, step, and jump, the following findings are obtained: The actions of the arms created a side-somersaulting angular momentum about the whole body center of gravity toward the side of the free leg during the support phase of the step, and a somersaulting angular momentum about the whole body center of gravity during each support phase. The action of the free leg created a somersaulting angular momentum about the whole body center of gravity during the support phases of the hop and step.

REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES

  • Chaudhary, Mahendra Pal;Choi, Junesang
    • Honam Mathematical Journal
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    • v.38 no.2
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    • pp.367-373
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    • 2016
  • Adiga and Anitha [1] investigated the Ramanujan's continued fraction (18) to present many interesting identities. Motivated by this work, by using known formulas, we also investigate the Ramanujan's continued fraction (18) to give certain relationships between the Ramanujan's continued fraction and the combinatorial partition identities given by Andrews et al. [3].

CERTAIN IDENTITIES ASSOCIATED WITH CHARACTER FORMULAS, CONTINUED FRACTION AND COMBINATORIAL PARTITION IDENTITIES

  • Chaudhary, M.P.;Choi, Junesang
    • East Asian mathematical journal
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    • v.32 no.5
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    • pp.609-619
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    • 2016
  • Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.

NOTE ON SOME CHARACTER FORMULAS

  • Chaudhary, Mahendra Pal;Chaudhary, Sangeeta;Choi, Junesang
    • Honam Mathematical Journal
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    • v.38 no.4
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    • pp.809-818
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    • 2016
  • Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 identities which are chosen among the above-mentioned 14 formulas.

An Efficient Computation of Matrix Triple Products (삼중 행렬 곱셈의 효율적 연산)

  • Im, Eun-Jin
    • Journal of the Korea Society of Computer and Information
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    • v.11 no.3
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    • pp.141-149
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    • 2006
  • In this paper, we introduce an improved algorithm for computing matrix triple product that commonly arises in primal-dual optimization method. In computing $P=AHA^{t}$, we devise a single pass algorithm that exploits the block diagonal structure of the matrix H. This one-phase scheme requires fewer floating point operations and roughly half the memory of the generic two-phase algorithm, where the product is computed in two steps, computing first $Q=HA^{t}$ and then P=AQ. The one-phase scheme achieved speed-up of 2.04 on Intel Itanium II platform over the two-phase scheme. Based on memory latency and modeled cache miss rates, the performance improvement was evaluated through performance modeling. Our research has impact on performance tuning study of complex sparse matrix operations, while most of the previous work focused on performance tuning of basic operations.

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The Metabolites of a Marine Mollusk Mytilus edulis:- Isolation of Taurine and Compositions of Free Fatty Acids and Free Amino acids-

  • Cho, Yong-Jin;Son, Byeng-Wha;Choi, Hong-Dae
    • Natural Product Sciences
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    • v.1 no.1
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    • pp.5-9
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    • 1995
  • The metabolites of marine mollusk Mytilus edulis were isolated and characterized, revealing the presence of the rare free fatty acids and proteinogenic amino acids together with a non-proteinogenic free amino acid, taurine. The free fatty acids in this organism were particularly interesting for the presence of both unusual n-6 acid [20:4 (n-6)] and triple bond containing acid (2,5-octadecadiynoic acid). In addition to the proteinogenic amino acids commonly found in proteins, non-proteinogenic free amino acid taurine was isolated and the structure was determined by its physicochemical properties. Recently taurine has been given much interest in the molecular level because of diverse biological activities and the medicinal properties. Furthermore, the result of the analyses of analyses of free amino acids showed that glycine, glutamic acid, serine and alanine, which were considered to be related to the taste of this organism, are predominantly present.

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TRIPLE AND FIFTH PRODUCT OF DIVISOR FUNCTIONS AND TREE MODEL

  • KIM, DAEYEOUL;CHEONG, CHEOLJO;PARK, HWASIN
    • Journal of applied mathematics & informatics
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    • v.34 no.1_2
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    • pp.145-156
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    • 2016
  • It is known that certain convolution sums can be expressed as a combination of divisor functions and Bernoulli formula. In this article, we consider relationship between fifth-order combinatoric convolution sums of divisor functions and Bernoulli polynomials. As applications of these identities, we give a concrete interpretation in terms of the procedural modeling method.

ON THE INDEX AND BIDERIVATIONS OF SIMPLE MALCEV ALGEBRAS

  • Yahya, Abdelaziz Ben;Boulmane, Said
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.385-397
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    • 2022
  • Let (M, [ , ]) be a finite dimensional Malcev algebra over an algebraically closed field 𝔽 of characteristic 0. We first prove that, (M, [ , ]) (with [M, M] ≠ 0) is simple if and only if ind(M) = 1 (i.e., M admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.

The Surface Roughness of Aluminium Material according to Cutting Conditions in the CNC Lathe Working (CNC 선반가공(旋盤加工)에서 절삭조건(切削條件)에 따른 알루미늄의 표면(表面)거칠기 변화(變化))

  • Kim, Tae-Wook;Son, Ki-Dong
    • Journal of the Korean Society of Industry Convergence
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    • v.5 no.3
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    • pp.201-208
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    • 2002
  • The machine tool which operates by hand is replacing by CNC machine tool to improve the quality of the product and the productivity in modem mechanic industry. The precision of machine part is influenced greatly the surface roughness by cutting condition of machine tool. So this study was performed to examine the aluminium surface roughness of section according to change of strength rating, nose radius, cutting speed, using live center. The results of this study are as follows; 1. In the case of 56mm diameter of test piece(length is below triple of diameter), whether establish the live center or not, doesn't influence to the surface roughness, and it is possible to make product without the live center. 2. The average surface roughness of 42mm diameter(length is quadruple of diameter) is similar to the 56mm diameter in the cutting condition of nose radius 0.8mm and cutting speed 140mm/min, but there are increases and differences in other cutting conditions. 3. In the case of test piece length more 70m/min(140m/mm) and nose radius improved greatly using the live center. 4. In the case of test piece length is quintuple of diameter, the nose radius must choose big tool and increase the cutting speed in preference live center establishment availability to improve that is surface roughness. Conclusively, if aluminum test piece length is fewer than triple of diameter, can process without establishing live center. If aluminum test piece length is more than quintuple of diameter, cutting conditions to improve surface roughness are (1) cutting speed (2) nose radius (3) whether the live center uses or not.

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