We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze group invariant generalized functions in this setting. Mathematics Subject Classification (2000): Primary: 46F30; secondary: 46T30, 35A30, 58E40

We introduce osp(m|n) spin Calogero models and find that the models have the symmetry of osp(m|n) half-loop algebra if and only if the coupling constant of the model equals to 2 m−n−4 . Mathematics Subject Classifications (2000): 70H06, 81R12, 17B70.

A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for obtaining new conservation laws from a given one. Mathematics Subject Classification (2000): 35Q53, 35Q58, 37K10

Our paper analyzes some new lines to advance on quickly evolving concepts, as the so-called Symmetry and Entropy, on graphs and networks in general. So, it will be very necessary to analyze the mutual relationship between some fuzzy measures, with their interesting applications; in particular, when we works on Complex Networks and Systems. 2000 Mathematics Subject Classification: 03B52, 03E72, ...

The Galilei group has been taken as the fundamental symmetry for 'nonrelativistic' physics, quantum or classical. Our fully theoretical formulation approach to theory asks some adjustments. We present a sketch of full picture here, emphasizing aspects that are different from more familiar picture. analysis involves careful treatment relation between exact mathematics and its physical applicatio...

We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces. 2000 Mathematics Subject Classification. Primary 53A10; Secondary 49Q05, 53C42.

Optimization problems appear in economics, mathematics, to name only a few areas. They refer to minimizing, respectively maximizing a certain functional under several constraints. These problems are also connected with rearrangements. Often times the minimizers, or maximizers satisfy certain symmetry and monotonicity conditions, i.e. increasing or decreasing. For (X,μ) a measure space, and F a ...

Invariance plays an essential role in Physics and Mathematics. It has a close connection between symmetry conserved quantity. In general any of the Lagrangian as well Hamiltonian corresponds to quantity, vice versa. This elegant works were first discussed formalized by Emmy Neother. this study analogy is shown invariance, conservation laws.

Zeros of the nth moment of the partition function [Z] are investigated in a vanishing temperature limit β → ∞, n → 0 keeping y = βn ∼ O(1). In this limit, the moment parameterized by y characterizes the distribution of the ground-state energy. We numerically investigate the zeros for ±J Ising spin glass models with tree and other several systems, which can be carried out with a feasible computa...

In this paper the dynamical noninvariance group SO(4, 2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little gr...