performing fast and accurate methods for modeling the electrical machines has been the subject of several studies and many authors proposed different procedures to attain this aim. beside the accuracy, the speed of the method is of great concern. on the other hand, the capability of the method to be changed according to the need is another important issue. finite element method provides relativ...

We consider random conformally invariant paths in the complex plane (SLEs). Using the Coulomb gas method in conformal field theory, we rederive the mixed multifractal exponents associated with both the harmonic measure and winding (rotation or monodromy) near such critical curves, previously obtained by quantum gravity methods. The results also extend to the general cases of harmonic measure mo...

For a continuous complex-valued function g on the real line without zeros, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of detG. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.

In these notes we review the method to construct integrable deformations of the compactified c = 1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The method is based on the formulation of the string theory as a matrix model. The flows generated by either momentum or winding modes (but not both) are inte...

usually both ends of a transformer winding are at the same side of the magnetic core. with this arrangement there are automaticaly the same number of the turns for each winding in both core windows next to the middle leg of a three phase three leg core type transformer. contrary to this arrangement it is possible to put the two ends of a winding at the different sides of the core. in this case ...