Hurwitz spaces of Galois coverings of P^1 with Galois groups Weyl groups

We prove the irreducibility of the Hurwitz spaces which parametrize Galois coverings of P^1 whose Galois group is an arbitrary Weyl group and the local monodromies are reflections. This generalizes a classical theorem due to Clebsch and Hurwitz.Comment: Latex, 15 page

Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds

We prove that the moduli spaces A_3(D) of polarized abelian threefolds with polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves of degree 2 or 3 and on the study of the corresponding period mappings associated with holomorphic differentials with trace 0. In particular we prove the unirationality of the Hurwitz space H_{3,A}(Y) which parameterizes simply branched triple coverings of an elliptic curve Y with determinants of the Tschirnhausen modules isomorphic to A^{-1}.Comment: 43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicat

Irreducibility of Hurwitz spaces

Graber, Harris and Starr proved, when n >= 2d, the irreducibility of the Hurwitz space H^0_{d,n}(Y) which parametrizes degree d coverings of a smooth, projective curve Y of positive genus, simply branched in n points, with full monodromy group S_d (math.AG/0205056). We sharpen this result and prove that H^0_{d,n}(Y) is irreducible if n >= max{2,2d-4} and in the case of elliptic Y if n >= max{2,2d-6}. We extend the result to coverings simply branched in all but one point of the discriminant. Fixing the ramification multiplicities over the special point we prove that the corresponding Hurwitz space is irreducible if the number of simply branched points is >= 2d-2. We study also simply branched coverings with monodromy group different from S_d and when n is large enough determine the corresponding connected components of H_{d,n}(Y). Our results are based on explicit calculation of the braid moves associated with the standard generators of the n-strand braid group of Y.Comment: latex2e, 34 pages, 5 figure

Robust fault-tolerant control

There are two main approaches to fault-tolerant control: passive and active.This thesis presents both methods for passive and for active FTC

Polarization types of isogenous Prym-Tyurin varieties

Let p:C-->Y be a covering of smooth, projective curves which is a composition of \pi:C-->C' of degree 2 and g:C'-->Y of degree n. Let f:X-->Y be the covering of degree 2^n, where the curve X parametrizes the liftings in C^{(n)} of the fibers of g:C'-->Y. Let P(X,\delta) be the associated Prym-Tyurin variety, known to be isogenous to the Prym variety P(C,C'). Most of the results in the paper focus on calculating the polarization type of the restriction of the canonical polarization of JX on P(X,\delta). We obtain the polarization type when n=3. When Y=P^1 we conjecture that P(X,\delta) is isomorphic to the dual of the Prym variety P(C,C'). This was known when n=2, we prove it when n=3, and for arbitrary n if \pi:C-->C' is \'{e}tale. Similar results are obtained for some other types of coverings.Comment: 28 page

A Bank of Reconfigurable LQG Controllers for Linear Systems Subjected to Failures

An approach for controller reconfiguration is presented. The starting point in the analysis is a sufficiently accurate continuous linear time-invariant (LTI) model of the nominal system. Based on a bank of reconfigurable LQG controllers, each designed for a particular combination of total faults, the reconfiguration consists of two operation modes. In the first mode a switching is invoked towards one of the pre-designed LQG controllers on the basis of the information about only the combination of total faults that is in effect. In the second mode, which is activated in cases of partial and component faults, a dynamic correction procedure is initiated which tries to reconfigure the currently active controller in such a way, that the failed closed-loop system remains stable and its performance is as close as possible to the performance of the closed-loop system with only total faults present in the system. In cases of partial faults the second mode is practically an extension of the modified pseudo-inverse method. In cases of component faults the second mode is based on an LMI optimization problem. The approach is illustrated using a model of a real-life space robot manipulator, in which total, partial and component faults are simulate

Using Collider Event Topology in the Search for the Six-Jet Decay of Top Quark-Antiquark Pairs

We investigate the use of the event topology as a tool in the search for the six-jet decay of top-pair production in proton-antiproton collisions at 1.8 TeV. Modified Fox-Wolfram "shape" variables, H_i, are employed to help distinguish the top-pair signal from the ordinary QCD multi-jet background. The H's can be constructed directly from the calorimeter cells or from jets. Events are required to lie in a region of H-space defined by L_i < H_i < R_i for i=1,...,,6, where the left, L_i, and right, R_i, cuts are determined by a genetic algorithm (GA) procedure to maximize the signal over the square root of the background. We are able to reduce the background over the signal to less than a factor of 100 using purely topological methods without using jet multiplicity cuts and without the aid of b-quark tagging.Comment: LaTeX, 19 pages, 13 figure

WHY TRUMP WON THE ELECTIONS – IN VIEW OF THE PROSPECT THEORY

In view of the behavioral approach and the prospect theory, the article tries to explain why an alternative is sometimes chosen, which compared to other options, leads to a worse and more uncertain expected outcome. The example analyzed is D. Trump’s victory in the US presidential elections in 2016. The reasons why he won lie in the candidate’s right strategy which takes into account the voting behaviour, and especially in the proper communication with voters, in the reflection effect and loss aversion. The validity of the prospect theory is sought not only in the political choices but also by means of a number of own studies examining its basic assumptions in Bulgarian conditions. Examples are given of applications in other fields