Constructing Involutive Tableaux with Guillemin Normal Form

Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan-K\"ahler theorem. Guillemin normal form establishes that the prolonged symbol of an involutive system admits a commutativity property on certain subspaces of the prolonged tableau. This article examines Guillemin normal form in detail, aiming at a more systematic approach to classifying involutive systems. The main result is an explicit quadratic condition for involutivity of the type suggested but not completed in Chapter IV, \S 5 of the book Exterior Differential Systems by Bryant, Chern, Gardner, Goldschmidt, and Griffiths. This condition enhances Guillemin normal form and characterizes involutive tableaux.Comment: This article co-evolved with "Degeneracy of the Characteristic Variety," arXiv:1410.6947 and most notation is shared. However, be aware that the meaning of the indices i,j,k,l and the space Y is not the same between these article

The Presidency, War, and Foreign Affairs: Practice Under the Framers

Varje år träder ca 50 000 människor ur Svenska kyrkan och avsäger sig därmed rätten att begravas i Svenska kyrkans ceremoniella ordning och lokaler. Man träder ut ur kyrkans ordning, och ut ur kyrkans rum, men man träder inte in i något annat. Mitt kandidatarbete är ett försök att visa på en annan ordning och andra rum. Every year some 50 000 people exits the Swedish Church and disclaims thus the right to be buried in the Swedish Church ceremonial order and premises. They leave behind the order of the Church, and exits the church room, but they do not enter anything else. My graduate work is an attempt to present an alternative order and alternative rooms

Assessment of Health and Nutritional Status Under the Integrated Child Development Services: in the Field Practice Area of Rural Training Health Centre, Nadayara, Travancore Medical College, Kollam-India

Assessment of health and nutritional status was carried out in Anganwadi Children in the Field Practice Area of Rural Training Health Centre, Nadayara, Travancore Medical College, Kollam. This is a cross sectional study within community base setting. Data were collected by a pretested structured questionnaire and analyzed by applying SPSS. Undernourished children in the Anganwadis under study were 21 %. Growth pattern of these children were significantly associated with the birth weight and the episodes of diarrhea. A significant proportion of children are missing the booster doses. DPT booster (16-24 months) is only 74.1 % and DT booster (5-6 years) is only a meager of 13.6

The Pierre Auger Observatory: Results on Ultra-High Energy Cosmic Rays

The focus of this article is on recent results on ultra-high energy cosmic rays obtained with the Pierre Auger Observatory. The world's largest instrument of this type and its performance are described. The observations presented here include the energy spectrum, the primary particle composition, limits on the fluxes of photons and neutrinos and a discussion of the anisotropic distribution of the arrival directions of the most energetic particles. Finally, plans for the construction of a Northern Auger Observatory in Colorado, USA, are discussed.Comment: Proceedings of the International Workshop on Advances in Cosmic Ray Science, Waseda University, Shinjuku, Tokyo, Japan, March 2008; to be published in the Journal of the Physical Society of Japan (JPSJ) supplemen

Novel applications of plant tissue culture and conventional breeding techniques to space biology research

In the minds of many, plant cell and tissue culture may now be viewed as a well-developed technology. It has been all but reduced to a tool to solve practical problems and contribute to plant improvement. While this is so in some instances, it is definitely not so in trying to utilize and integrate plant cell and tissue culture into the projected needs of Space biology programs. This is not merely because of the challenges posed by the unusual physical environment of Space such as microgravity, or the constraints posed by Spaceflight protocols but is due to our inadequate knowledge of the factors that control plant growth and development, including systems as they grow in vitro. The premature (and in many cases unrealistically optimistic) initial assessments of what is really known about what happens in aseptic culture belies the many fundamental developmental and physiological questions that still need to be answered before plan