We introduce ^-analogues of Clifford and Weyl algebras. Using these, we construct spinor and oscillator representations of quantum enveloping algebras of type A N ^1,B N ,C N ,D N and ^-I Also w e discuss the irreducibility and the unitarity of these representations.

Aim:The aim of the present study was to examine the relationship between depressive mood and diagnostic components of sarcopenia. Methods:The study used baseline data of participants in the Toyota Prevention Intervention for Cognitive Decline and Sarcopenia study. Participants in this cross-sectional study were 432 older adults (46.5% women, mean age 72.5 AE 4.7 years). We defined sarcopenia using the diagnostic algorithm recommended by the Asian Working Group for Sarcopenia, and all participants were classified into a sarcopenia or healthy control group. The skeletal muscle mass was measured by bioelectrical impedance. Depressive mood was assessed using the Geriatric Depression Scale-15 (range 0-15).Results: Among the 432 participants, 9.5% were classified as having sarcopenia. The mean AE SD Geriatric Depression Scale-15 scores in the control and sarcopenia groups were significantly different at 3.9 AE 2.8 and 5.3 AE 3.3, respectively (P = 0.003). Furthermore, depressive mood was significantly more prevalent in the sarcopenia group (P = 0.011). Multiple linear regression analysis showed that the Geriatric Depression Scale score was associated with grip strength (β = −0.23, P = 0.004) and walking speed (β = −0.15, P = 0.006), but not skeletal muscle mass index (β = −0.16, P = 0.142), after controlling for demographic factors, chronic diseases, inflammatory markers and physical activity.Conclusions: Sarcopenia was associated with depressive mood. In terms of the diagnostic components of sarcopenia, depressive mood was not associated with decreased muscle mass, but was associated with low muscle strength and low physical performance.

We construct coordinate algebras of quantum orthogonal, special orthogonal and symplectic groups using M. Jimbo's solutions of the Yang-Baxter equation and determine their Peter-Weyl decompositions. To do this, we study some class of bialgebras and their group-like elements (quantum determinants). A new realization of the universal ^-matrix is also given.

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