• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.301-320
• /
• 2008

The smash product algebra has been generalized to general smash product algebra in [3] and we can generalize the smash coproduct coalgebra to obtain the general smash coproduct coalgebra. It is natural to replace the smash product and smash coproduct by the generalized smash product and generalized smash coproduct and consider the condition under which the generalized smash product algebra structure and the generalized smash coproduct coalgebra structure will inherit a bialgebra structure or a Hopf algebra structure. We derive necessary sufficient conditions for the problem. This generalizes the corresponding results in [7] and [4].

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.1
• /
• pp.57-60
• /
• 2006

Several examples of smash product are given.

• Korean Journal of Applied Biomechanics
• /
• v.23 no.3
• /
• pp.201-208
• /
• 2013

The aim of this study was to investigate badminton smash and drop motion depends on player's level. To perform this study, ten male badminton players were participated: five skilled players (SG, age: $21.6{\pm}1.1$ yrs, height: $181.4{\pm}6.8$ cm, body mass: $72.4{\pm}5.7$ kg, career: $11.2{\pm}1.1$ yrs) and five less-skilled players (LSG, age: $21.2{\pm}1.1$ yrs, height: $180.2{\pm}5.6$ cm, body mass: $73.6{\pm}6.7$ kg, career: $10.6{\pm}0.9$ yrs). Three-dimensional motion analysis with 7 infrared cameras was performed with a sampling frequency as 200 Hz. Player's swing motion was divided into four events: starting motion (E1), backswing (E2), impact (E3), following (E4). For all upper joints, LSG showed greater angle differences between drop and smash motions than that of SG at E3 (p<.05). For all upper joints, greater angular velocities were found in SG than that of LSG. For both groups, significantly smaller angular velocities were found in drop motion than that of smash motion (p<.05). The greater sequential angular velocities (proximal to distal) were found in SG than LSG during smash motion. Based on our findings, performing the same motion between drop and smash would be related to enhance performance at badminton competition. It is expected that these results will be useful in developing a training program for enhancing performance of badminton athletes.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.337-342
• /
• 1999

M. Cohen and S. Montgomery showed that a Maschke-type theorem for the smash product, which unlike the corresponding result for group actions, does not require any assumptions about the characterstic of the algebra. Our purpose in this paper is a Maschke-type theorem for the graded smash coproduct C⋊kG: let V be a right C⋊kG-comodule and W a C⋊kG-subcomoduleof V which is a C-direct summand of V. Then W is a C⋊kG-direct summand of V. Also this result is equivalent to the following : let V be a graded right C-comodule and W a graded subcomodule of V which has a complement as a C-subcomodule of V. Then W has a graded complement.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.99-113
• /
• 1998

Let (H, K) be a paired Hopf algebras and let A be arbitrary left H-module coalgebra. We construct twisting coproduct on $A{\otimes}K$. We show that the well known construction of the smash coproduct can be viewed as a particular case of the construction above.

• Trans-
• /
• v.8
• /
• pp.79-93
• /
• 2020

The main purpose of this article is to discuss the impact of "Dance Smash" TV show on Chinese dance, which uses the combination of dance and new media technology as the core content of the program. "Dance Smash", as a dance communication TV program for the public, first considers the entertainment attributes of variety shows. Spread the dance art on the basis of meeting the public's aesthetic needs, thereby expanding the popular living space of dance art. The use of 'moment of the storm' has let the general audience of non-dance majors feel the technical charm of dances, thus playing a healthy promotion role. However, whether "Bullet Time", a type of dance program that has had a successful case in the West, can also have a positive impact on the mass communication of dance in the localization of China, this is what questions and seeks of this article.

• Journal of the Chungcheong Mathematical Society
• /
• v.8 no.1
• /
• pp.173-181
• /
• 1995

Let H and G be finite dimensional semisimple Hopf algebras and let A and B be left H and G-module algebras respectively. We use smash product algebras to show that 1) if A is right Artinian then $A^H$ is right Artinian, 2) $Soc\;V_A{\subset}Soc\;V_{A^H}$ and rad $V_A{\supset}\;radV_{A^H}$, 3) $K\;dim\;_BV_A=K\;dim\;_{B^G}V_{A^H}$.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.527-541
• /
• 2001

We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).

• Korean Journal of Applied Biomechanics
• /
• v.18 no.1
• /
• pp.11-19
• /
• 2008

This study was conducted with 8 male table tennis players who won national competitions. Of the subjects, 4 used a racket of penholder grip and 4 used one of shake hand grip, and all of them were right.handers. We analyzed three-dimensional angular characteristics such as angular component, swing trajectory and swing posture related to the racket swing motions of forehand drive and smash in table tennis, and drew conclusions as follows. Racket angle(p<.05) and racket swing angle(p<.01) were significantly different between the two motions. In smash, the back swing posture maintained the racket angle large by holding the racket upright and made the racket swing angle small for high ball speed. In addition, the height of the racket head in back swing posture was also significantly different between the two motions. In phg on impact, the open angle of the long axis of the racket was significantly different between the two motions. This shows that impact was applied a bit behind for giving top spin to the ball. In the back swing of drive, the gradient of the upper body was slightly larger in shg than in phg probably because of the structural difference of the racket grip in the neutral posture.

• Korean Journal of Applied Biomechanics
• /
• v.13 no.2
• /
• pp.65-74
• /
• 2003

The purpose of this study was to analyze kinematic variables in the badminton smash motion through 3-dimensional image analysis. The kinematic variables were velocity of joints in upper limbs, the angle of wrist in the impact, and the angular velocity of the top of racket head. The smash motions of four male badminton players in H University and four male students at department of the physical education in K University who were not majoring in badminton were analyzed kinematically and the attained conclusions were as follow. 1. The velocity of segments in upper limbs of the unskilled group was faster than that of the skilled group. The movement pattern was fast back swing-slow impact moment-fast fellow through in the unskilled group, but slow back swing-fast impact moment-slow follow through in the sullied group. 2. As the BS phases, the velocity of segment in right shoulder was different significantly between groups. Right elbow and right wrist segments, velocity of racket head was different significantly between groups(p<.05) by IP phases. As the FT phases, there was no significant difference. 3. The angle of right wrist at the impact, the angle of palm flexion and the angle of palm flexion in aspect were shown that the skilled group was higher than unskilled group. There was no significant difference. 4. The velocity of racket head was shown that the unskilled group has fast velocity, but the angle velocity was shown the unskilled group has slow. 5. The angle velocity of racket head in aspect were no significant difference between groups, but maximal angle velocity was different significantly between groups(p<.05).