We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and their corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.

Address of President Taft at the Fifteenth International Congress on Hygiene and Demography ........................... 504 Twelfth Annual Intercollegiate Excursion of New England .......................... 508 The Study of Malaria .................... 509 The Eskimos of Coronation Gulf ........... 510 Betirement of Professor Henry Shaler Williams .............................. 510 Scientific N...

We give a Decomposition Theorem for a family of Hopf algebras containing the well-know family of Taft Hopf algebras. Therefore, those indecomposable codes over this family of algebras (cf. [4]) is an indecomposable code over the studied case. We use properties of Hopf algebras to show that dual (in the module sense) of an ideal code is again an ideal code.

BACKGROUND Treatment of lateral fractures of the clavicle is challenging and has been controversially discussed for a long time due to high non-union rates in non-operative treatment and high complication rates in surgical treatment. Acromioclavicular joint instability due to the injury of the closely neighbored coraco-clavicular ligaments can result in a cranialization of the medial clavicle s...

22 VOL. 47 NO. 3 2013 ACTA MEDICA PHILIPPINA _______________ Corresponding author: Mark Anthony S. Sandoval, MD Section of Endocrinology, Diabetes and Metabolism Medical Research Laboratory Philippine General Hospital Taft Avenue, Ermita, Manila 1000 Philippines Telephone: 0916-5921818 E-mail: [email protected] Effect of Malunggay (Moringa oleifera) Capsules on Lipid and Glucose Le...

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