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 ...

the frequency response analysis (fra) test has been recognized as one of the sensitive tools available for detecting electrical and mechanical faults inside power transformers. however, there is still no universally systematic interpretation technique for these tests. many research efforts have employed different statistical criteria in order to aid the interpretative capability of the fra, but...

Correlation functions of one-unit spectral flowed states in string theory on AdS3 are considered. We present a formalism which allows to explicitly find the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by amplitudes of states in w = 1 sectors. We give a precise prescription to solve this system of linear differential equations in cases that are relevant to obtain th...

Analysing closed string tachyon condensation will improve our understanding of spacetime in string theory. We study the string spectrum on a BTZ black hole spacetime supported by NS-NS flux, which provides a calculable example where we would expect to find a quasi-localised tachyon. We find that there is a winding tachyon when the black hole horizon is smaller than the string scale, as expected...