Floer theory assigns, in favourable circumstances, an abelian group HF (L0, L1) to a pair (L0, L1) of Lagrangian submanifolds of a symplectic manifold (M,ω). This group is a qualitative invariant, which remains unchanged under suitable deformations of L0 or L1. Following Floer [7] one can equip HF (L0, L1) with a canonical relative Z/N -grading, where 1 ≤ N ≤ ∞ is a number which depends on (M,ω...

We consider Γ-graded commutative algebras, where Γ is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on the subject. We then give a recent classification result and formulate an open problem.

The formalism of graded Poisson-sigma models allows the construction of N = (2, 2) dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions , is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of super...

Using colored superanalysis and ε-Lie superalgebras, we build the minimal Poincaré superalgebra in the case of the Z n grading. We then build a representation of this algebra, and the corresponding Poincaré supergroup.

We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on the bilipschitz equivalence types of the pieces in the standard (resp. minimal) tree-graded structure. In particular, the asymptotic cones of many relatively hyperbolic groups do not depend on the ...

The structure of graded triangular algebras T of arbitrary dimension are studied in this paper. This is motivated in part for the important role that triangular algebras play in the study of oriented graphs, upper triangular matrix algebras or nest algebras. It is shown that T decomposes as T = U + ( ∑ i∈I Ti), where U is an R-submodule contained in the 0-homogeneous component and any Ti a well...

Thermoelastic simulation of functionally graded materials is practically important for engineers. Here, the extension and assembly of our two previous papers (Computational Mechanics 2006, 38, p51-60; Engineering Analysis with Boundary Elements 2008, 32, p704-712) is presented to evaluate the transient temperature and stress distributions in two-dimensional functionally graded solids. In this c...

Conventional metallic foam processing seeks to maximize uniformity in pore size, relative density, and other aspects of foam structure in order to minimize property variation associated with the statistical nature of foams, and thereby increase their reliability in service. However, property uniformity is in many cases an inefficient approach to meeting overall design criteria, as demonstrated ...