An operadic approach to deformation quantization of compatible Poisson brackets, I

An analogue of the Livernet–Loday operad for two compatible brackets, which is a flat deformation of the bi-Hamiltonian operad is constructed. The Liver net–Lo day operad can be used to define ?-products and deformation quantization for Poisson structures. The constructed operad is used in the same way, introducing a definition of operadic deformation quantization of compatible Poisson structures.

Some constructions of deformation quantization are known now for the case which was the most important for, namely the algebra of functions on a smooth Poisson manifold; see, for example, the work of Kontsevich. It seems to be much more difficult to deal with deformation quantization of two compatible Poisson brackets – even on the level of introducing the problem and giving the necessary definitions.

Assessing the Lifestyle of an Extinct Animal Studying its Automatic Nervous System

The titannosaurs became extinct 66 million years ago. Their size restricted their mobility, thermo regulation and blood supply to the organs. The study deployed modeling techniques and statistics to assess the prehistoric physiology, size, metabolism and organ function. 

The Automatic nervous system ensured blood flow to the brain through muscle contraction and special boney structures in the neck called cervical ribs. In order to keep face with the huge metabolic needs of the body, the animal could sleep for only 3 hrs a day and had very high body temperatures which increased with activity. There was an in-built cooling mechanism in their carotid arteries to preserve the brain function. This study identified that growth-lines in osteons in the anterior process of the rib grew faster than dense bone and juveniles grew faster than adults Power spectral analyses of growth intervals in osteons showed a ratio of 1.3 (LF/HF) and for bone 1.4 (LF/HF) NS.The life span of the animal was 100 years.

Download PDF