We discuss the fermion couplings in a four dimensional SU(2) linear moose model by allowing for direct couplings between the left-handed fermions on the boundary and the gauge fields in the internal sites. This is realized by means of a product of non linear σ-model scalar fields which, in the continuum limit, is equivalent to a Wilson line. The effect of these new non local couplings is a cont...

We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs of relatively hyperbolic groups, and to construct the first example of finitely generated group with a ...

We describe a variational problem on a surface under a constraintof geometrical character. Necessary and sufficient conditions for the existence ofbifurcation points are provided. In local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. The problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

[t]he analysis of the phrase “how many” unambiguously leads to a definite meaning for the question [“How many different sets of integers do their exist?”]: the problem is to find out which one of the א ‟s is the number of points of a straight line... Cantor, after having proved that this number is greater than א0, conjectured that it is א1. An equivalent proposition is this: any infinite subset...

We study the spin-1/2 chain with nearest neighbor (κ1) and next-nearest neighbor (κ2) interactions in the regime κ2 ≫ κ1, which is equivalent to two chains with a ‘zig-zag’ interaction. In the continuum limit, this system is described in term of two coupled level-1 WZW field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used...

In this research, the influence of structure on the tensile properties of single- walled carbon nanotubes (CNTs) is evaluated using molecular mechanics technique and finite element method. The effects of diameter, length and chiral angle on elastic modulus and Poisson’s ratio of armchair, zigzag and chiral structures are investigated. To simulate the CNTs, a 3D FEM code is developed using the A...