On braid monodromy factorizations

We introduce and develop a language of semigroups over the braid groups for a study of braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application we give a new proof of Orevkov's theorem on realization of a bmf over a disc by algebraic curves and show that the complexity of such a realization can not be bounded in terms of the types of the factors of the bmf. Besides, we prove that the type of a bmf is distinguishing Hurwitz curves with singularities of inseparable types up to $H$-isotopy and $J$-holomorphic cuspidal curves in \C P^2 up to symplectic isotopy.Comment: 52 pages, AMS-Te

Generic coverings of plane with A-D-E-singularities

We generalize results of the paper math.AG/9803144, in which Chisini's conjecture on the unique reconstruction of f by the curve B is investigated. For this fibre products of generic coverings are studied. The main inequality bounding the degree of a covering in the case of existence of two nonequivalent coverings with the branch curve B is obtained. This inequality is used for the proof of the Chisini conjecture for m-canonical coverings of surfaces of general type for $m\ge 5$.Comment: 43 pages, 20 figures; to appear in Izvestiya Mat

Critical behavior of disordered systems with replica symmetry breaking

A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the one-step replica symmetry breaking, fixed points of the renormalization group equations are found using the Pade-Borel summing technique. For every value $p$, the threshold dimensions of the system that separate the regions of different types of the critical behavior are found by analyzing those fixed points. Specific features of the critical behavior determined by the replica symmetry breaking are described. The results are compared with those obtained by the $\epsilon$-expansion and the scope of the method applicability is determined.Comment: 18 pages, 2 figure

Kelayakan Media Buku Saku Submateri Manfaat Keanekaragaman Hayati di Kelas X SMA Mandor

This research aimed to show the feasibility of learning medium in the form of pocket book on biodiversity submaterial in 10th Grade of SMA. Pocket book medium was tested its feasibility by five validators, they were two lecturers of FKIP UNTAN Biology Education Study Program and three High School Biology Teachers. Research instrument was used validation sheet and school partner selection technique was used purposive sampling, those selected schools were SMA Negeri 1 Mandor, SMA Negeri 3 Mandor, and SMA Bina Setia Sekilap. There were three aspects on which the validators assigned, those were format aspect, content aspect, and language aspect. From validation result, the pocket book was stated as valid and feasible to use with the average score of 3,6