We analyze those integrable statistical systems which originate from some relevant
perturbations of the minimal models of conformal field theories. When only massive …

To a given tiling a noncommutative space and the corresponding C*-algebra are
constructed. This includes the definition of a topology on the groupoid induced by …

Is there a vector space whose dimension is the golden ratio? Of course not--the golden ratio
is not an integer! But this can happen for generalizations of vector spaces--objects of a …

Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …

Entropy is a concept which appears in several fields and it is in the center of interest both in
mathematical and physical subjects, sometimes even at other places, for example in …

Coassociativity of∆ follows from associativity of the product in G. To see that the cancellation
property holds, note that (A⊗ 1)∆(A) is the unital∗-subalgebra of C (G× G) spanned by all …

Bayes' rule, P (B| A) P (A)= P (A| B) P (B), is one of the simplest yet most profound,
ubiquitous, and far-reaching results of classical probability theory, with applications in any …

Schubert polynomials were introduced by Bernstein et al. and Demazure, and were
extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an …

The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

We find a relation between the spectrum of solitons of massive N= 2 quantum field theories
in d= 2 and the scaling dimensions of chiral fields at the conformal point. The condition that …