278 research outputs found
The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows
For integrable Hamiltonian systems with two degrees of freedom whose
Hamiltonian vector fields have incomplete flows, an analogue of the Liouville
theorem is established. A canonical Liouville fibration is defined by means of
an "exact" 2-parameter family of flat polygons equipped with certain pairing of
sides. For the integrable Hamiltonian systems given by the vector field
on where
is a complex polynomial in 2 variables, geometric properties of
Liouville fibrations are described.Comment: 6 page
Connected components of spaces of Morse functions with fixed critical points
Let be a smooth closed orientable surface and be the space
of Morse functions on having exactly critical points of local minima,
saddle critical points, and critical points of local maxima,
moreover all the points are fixed. Let be the connected component of a
function in . By means of the winding number introduced by Reinhart
(1960), a surjection is constructed. In
particular, , and the Dehn twist about the boundary of any
disk containing exactly two critical points, exactly one of which is a saddle
point, does not preserve . Let be the group of orientation
preserving diffeomorphisms of leaving fixed the critical points, be the connected component of in , and
the set of diffeomorphisms preserving
. Let be the subgroup of generated by
and all diffeomorphisms which preserve some
functions , and let be its subgroup
generated and the Dehn twists about the components of level
curves of functions . We prove that if , and construct an epimorphism
, by means of
the winding number. A finite polyhedral complex associated to the
space is defined. An epimorphism and finite generating sets for the groups
and in terms of the 2-skeleton of the complex
are constructed.Comment: 12 pages with 2 figures, in Russian, to be published in Vestnik
Moskov. Univ., a typo in theorem 1 is correcte
BUSINESS DECISION TRENDS IN THE INTELLECTUAL PRODUCTION DEVELOPMENT
The main trends have been described and the system characteristics of intellectual production have been presented: customization of products, integration of the product and the service it provides, the transition to integrated solutions and services, mass personification while reducing the share of costs per unit of output and customer waiting time for an order. The key components of the transformation of business management models in the fourth industrial revolution have been identified. Cross-correlation and regression analysis for indicators of high-tech production have been made. A basic, optimistic and pessimistic forecast of changes in the share of high-tech and technology products in the gross domestic product, depending on the growth of high-performance jobs, has been built. The analysis of the development of intellectual production presented in the article, as well as the results of modeling can be used in the construction of forecast trends of the economy in the transition to the fourth industrial revolution
Genetic structure analysis of leaf rust resistant triticale accessions from the VIR collection using gliadin patterns
The gliadin banding patterns of important accessions from the collection of the N. I. Vavilov All‑Russian Institute of Plant Genetic Resources (VIR) registered in the form of “protein formulas” provide reliable information for the preparation of a “protein passport” for each accession and is convenient for storage and computer processing. It helps to control originality and integrity of accessions during regeneration and their use in breeding. The study involved 17 triticale accessions resistant to leaf rust. The analysis was carried out on single grains of the original accession (a sample of 13–26 kernels) according to the standard protocol adopted by VIR and approved by the International Seed Testing Association (ISTA). The gliadin electrophoretic banding patterns of triticale accessions were registered in the form of “protein formulas”; polymorphism of each accession and genetic diversity within the collection were estimated, and genetic structure of accessions was identified based on the marker protein components. A large variety of the revealed genotypes opens a possibility to identify accessions that combine resistance with other useful traits. Stable and polymorphic accessions including from 2 to 7 biotypes were found. The discovery of interbiotype hybrids and recombinant genotypes in the composition of some polymorphic accessions indicates the instability of their genetic structure and the ongoing formation process. This is due to the heterogeneity of the original parental forms, the tendency to cross‑pollination and insufficiently thorough selection. The data on the triticale genotypic structure can be used in introgressive breeding to control the transfer of rye genetic material to wheat varieties in order to increase their immunity and resistance to adverse factors
Topology of the spaces of Morse functions on surfaces
Let be a smooth closed orientable surface, and let be the space of
Morse functions on such that at least critical points of each
function of are labeled by different labels (enumerated). Endow the space
with -topology. We prove the homotopy equivalence where is one of the manifolds , and the point in dependence on the sign of ,
and is the universal moduli space of framed Morse
functions, which is a smooth stratified manifold. Morse inequalities for the
Betti numbers of the space are obtained.Comment: 15 pages, in Russia
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