This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal...) and properly biological (heart beating, respiration, metabolic...). In particular, the role of bi...

Some of the major enhancements are eliminating head contention, reducing or eliminating nozzle changes, supporting user-defined nozzles, supporting large nozzles for holders 2 and 3, and being able to define multiple part data for a given part number. The cycle time improvement exceeds the original goal of 5%, and the result at one surface mount center was more than 16% over hand-created and op...

General relativity in three spacetime dimensions is used to explore three approaches to the “problem of time” in quantum gravity: the internal Schrödinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt equation, and covariant canonical quantization with “evolving constants of motion.” (To appear in Proc. of the Lanczos Centenary Conference, Raleigh, NC, December 1...

A 2-walk of a graph is a walk visiting every vertex at least once and at most twice. By generalizing decompositions of Tutte and Thomassen, Gao, Richter and Yu proved that every 3-connected planar graph contains a closed 2-walk such that all vertices visited twice are contained in 3separators. This seminal result generalizes Tutte’s theorem that every 4-connected planar graph is Hamiltonian as ...

What happens to the uncertainity relations along the process of gravitational collapses ? What is the position-space wave function of two finite volume massive bosons if we take contact interaction into account? What is the microscopic explanation in terms of particle exchanges of the force in the Casimir effect?

A connected Lie group G is generated by its two 1-parametric subgroups exp(tX), exp(tY ) if and only if the Lie algebra of G is generated by {X, Y }. We consider decompositions of elements of G into a product of such exponentials with times t > 0 and study the problem of minimizing the total time of the decompositions for a fixed element of G. We solve this problem for the group SU2 and describ...