S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the $S$-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic type systems. In particular, for the 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel package

The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type

We obtain the necessary and sufficient conditions for a two-component (2+1)-dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions. These conditions are in involution, implying that the systems in question are locally parametrized by 15 arbitrary constants. It is proved that all such systems possess three conservation laws of hydrodynamic type and, therefore, are symmetrizable in Godunov's sense. Moreover, all such systems are proved to possess a scalar pseudopotential which plays the role of the `dispersionless Lax pair'. We demonstrate that the class of two-component systems possessing a scalar pseudopotential is in fact identical with the class of systems possessing infinitely many hydrodynamic reductions, thus establishing the equivalence of the two possible definitions of the integrability. Explicit linearly degenerate examples are constructed.Comment: 15 page

On a class of second-order PDEs admitting partner symmetries

Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs with four variables, that possess partner symmetries and contain only second derivatives of the unknown. We present a general form of such a PDE together with recursion relations between partner symmetries. This general PDE is transformed to several simplest canonical forms containing the two heavenly equations of Plebanski among them and two other nonlinear equations which we call mixed heavenly equation and asymmetric heavenly equation. On an example of the mixed heavenly equation, we show how to use partner symmetries for obtaining noninvariant solutions of PDEs by a lift from invariant solutions. Finally, we present Ricci-flat self-dual metrics governed by solutions of the mixed heavenly equation and its Legendre transform.Comment: LaTeX2e, 26 pages. The contents change: Exact noninvariant solutions of the Legendre transformed mixed heavenly equation and Ricci-flat metrics governed by solutions of this equation are added. Eq. (6.10) on p. 14 is correcte

Target Energy Monitoring Method for the Analysis of Production Companies and Facilities of Housing and Communal Services

© Published under licence by IOP Publishing Ltd. This paper discusses the aspects of target energy monitoring structures at the production companies and facilities of housing and communal services

Engineering Background: Modern Formats and Challenges of Conceptual Engineering

© Published under licence by IOP Publishing Ltd. This paper describes the analysis of problems and development perspectives of engineering education in our and other countries. Special attention is given to modern formats of education that motivate creative efforts of engineers-to-be as well as issues of conceptual engineering taking the challenges of modernity into account

Instability of two interacting, quasi-monochromatic waves in shallow water

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr\"odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure

Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems

We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2+1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of the corresponding dispersive counterparts. Modulo the Miura group, such deformations are unique. The requirement that any hydrodynamic reduction possesses a deformation of this kind imposes strong constraints on the structure of dispersive terms, suggesting an alternative approach to the integrability in 2+1 dimensions.Comment: 18 pages, section adde

Y-chromosomal connection between Hungarians and geographically distant populations of the Ural Mountain region and West Siberia

Hungarians who live in Central Europe today are one of the westernmost Uralic speakers. Despite of the proposed Volga-Ural/West Siberian roots of the Hungarian language, the present-day Hungarian gene pool is highly similar to that of the surrounding Indo-European speaking populations. However, a limited portion of specific Y-chromosomal lineages from haplogroup N, sometimes associated with the spread of Uralic languages, link modern Hungarians with populations living close to the Ural Mountain range on the border of Europe and Asia. Here we investigate the paternal genetic connection between these spatially separated populations. We reconstruct the phylogeny of N3a4-Z1936 clade by using 33 high-coverage Y-chromosomal sequences and estimate the coalescent times of its sub-clades. We genotype close to 5000 samples from 46 Eurasian populations to show the presence of N3a4-B539 lineages among Hungarians and in the populations from Ural Mountain region, including Ob-Ugric-speakers from West Siberia who are geographically distant but linguistically closest to Hungarians. This sub-clade splits from its sister-branch N3a4-B535, frequent today among Northeast European Uralic speakers, 4000–5000 ya, which is in the time-frame of the proposed divergence of Ugric languages

Association of vascular endothelial growth factor B (VEGFВ) gene polymorphisms with intracranial aneurysms

Intracranial aneurysm (IA) is a complex disease resulting in subarachnoid hemorrhage (SAH) due to a rupture. The average worldwide prevalence of this disease is about 2–5 %, with 50 % of them ending in death or neurological disorders of varying severity, with a high probability of recurrence of hemorrhage during the frst half of the year after rupture. Subarachnoid hemorrhage is annually registered in at least 18 thousand people in Russia. Associations of polymorphic variants rs594942 and rs11603042 of the VEGFB gene in intracranial aneurysm development in the Volga-Ural region of the Russian Federation with the presence of the symptom complex of undifferentiated connective tissue dysplasia (uDST) and arterial hypertension (AH) were investigated. The C* allele rs594942 and rs11603042 of the VEGFB gene is a marker of an increased risk of IA as a whole (p = 0.025; χ2 = 5.052; OR = 1.32) in women as a whole (p = 0.001; χ2 = 10.124; OR = 1.70) and in comorbid state with uDCT (p = 0.002; χ2 = 9.501; OR = 2.34) and AG (p = 0.006; χ2 = 7.385; OR = 2.109). We found that the genotype *C*C of locus rs594942 of the VEGFB gene is a marker of an increased risk of intracranial aneurysm in general (p = 0.017; χ2 = 5.702; OR = 1.49) and among women in general (p = 0.0005; χ2 = 12.078; OR = 2.25) and with the symptomatic complex uCTD (p = 0.007; χ2 = 7.173; OR = 2.67) and AH (p = 0.010; χ2 = 6.471; OR = 2.51). We have obtained new results on the role of polymorphic variants of the VEGFB gene in the formation of intracranial aneurysm, taking into account the presence of the symptom complex uDCT and AH among the residents of the Volga-Ural region of Russia. A burdened comorbid background and the presence of undifferentiated connective tissue dysplasia and arterial hypertension can contribute to an increased risk of intracranial aneurysm, as evidenced by the results of our study