Reconstruction of Planar Domains from Partial Integral Measurements

We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear differential equation with polynomial coefficients. This includes domains with piecewise-algebraic and, in particular, piecewise-polynomial boundaries. Our approach is based on one-dimensional reconstruction method of [Bat]* and a kind of "separation of variables" which reduces the planar problem to two one-dimensional problems, one of them parametric. Several explicit examples of reconstruction are given. Another main topic of the paper concerns "invisible sets" for various types of incomplete moment measurements. We suggest a certain point of view which stresses remarkable similarity between several apparently unrelated problems. In particular, we discuss zero quadrature domains (invisible for harmonic polynomials), invisibility for powers of a given polynomial, and invisibility for complex moments (Wermer's theorem and further developments). The common property we would like to stress is a "rigidity" and symmetry of the invisible objects. * D.Batenkov, Moment inversion of piecewise D-finite functions, Inverse Problems 25 (2009) 105001Comment: Proceedings of Complex Analysis and Dynamical Systems V, 201

Accuracy of reconstruction of spike-trains with two near-colliding nodes

We consider a signal reconstruction problem for signals $F$ of the form $F(x)=\sum_{j=1}^{d}a_{j}\delta\left(x-x_{j}\right),$ from their moments $m_k(F)=\int x^kF(x)dx.$ We assume $m_k(F)$ to be known for $k=0,1,\ldots,N,$ with an absolute error not exceeding $\epsilon > 0$. We study the "geometry of error amplification" in reconstruction of $F$ from $m_k(F),$ in situations where two neighboring nodes $x_i$ and $x_{i+1}$ near-collide, i.e $x_{i+1}-x_i=h \ll 1$. We show that the error amplification is governed by certain algebraic curves $S_{F,i},$ in the parameter space of signals $F$, along which the first three moments $m_0,m_1,m_2$ remain constant

Несуществование некоторых Q-полиномиальных дистанционно регулярных графов

I. N. Belousov, A. A. Makhnev, and M. S. Nirova described Q-polynomial distance-regular graphs Γ of diameter 3 for which the graphs Γ2 and Γ3 are strongly regular. Set a = a3. A graph Γ has type (I) if c2 + 1 divides a, type (II) if c2 + 1 divides a + 1, and type (III) if c2 + 1 divides neither a nor a + 1. If Γ is a graph of type (II), then a + 1 = w(c2 + 1), t2 = w(w(c2 + 1) + c2), and either (i) w = s2, t2 = s2(s2(c2 + 1) + c2), (s2(c2 + 1) + c2 is the square of an integer u, c2 = (u2 − s2)/(s2 + 1), t = su, and a = (u2s2 − 1)/(s2 + 1) or (ii) c2 = sw, t2 = w2(sw + 1 + s), sw + 1 + s is the square of an integer u, c2 = (u2 − 1)w/(w + 1), t = uw, a = (u2w2 − 1)/(w + 1), and Γ has intersection array (equation presented) If a graph of type (IIii) is such that w = u, then it has intersection array {w4 + w − 1, w4 − w3, (w2 − w + 1)w; 1, w(w − 1), (w2 − w + 1)w2}. We prove that graphs with such intersection arrays do not exist for even w. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved

Methane Fluxes Into Atmosphere from Fennoskandian Lakes

The experimental data on methane fluxes into the atmosphere from Fennoscandian lakes is analyzed. The contribution made by the lake network of this northern region to the atmospheric methane budget is estimated as 320 +/- 23 KtCH(4) per year. From 16 to 37% of the annual methane emission from Fennoscandian lakes is carried out by methane produced during the ice cover period. The methane fluxe rate from studied lakes is estimated as 2.6 +/- 0.2 gCH(4)m(-2) yr(-1). Among lakes of the region, small lakes (areaPeer reviewe

Еколого - гігієнічні природоохоронні модулі - основа біобезпеки морегосподарської діятльності

В работе представлены гигиенически регламентированные природоохранные модули, разработанные на основе альтернативных видов энергии и безотходной технологии для практического применения в структурах морехозяйственной деятельности.Hygienically restricted nature-protective complexes worked out with alternative types of energy and waste-free technologies for practical use in the structures of maritime activity.В роботі представлені гігієнічно регламентовані природоохоронні модулі, що розроблені на основі альтернативних видів енергії і безвідходної технології для практичного застосування в структурах морегосподарської діяльності

Stratifications and foliations in phase portraits of gene network models

Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ensembles of trajectories of the corresponding dynamical systems, in particular, to estimate the highest likelihood domain of the initial data, to solve inverse problems of parameter identification, to list the equilibrium points and their characteristics, to localize cycles in the phase portraits, to construct stratification of the phase portraits to subdomains with different qualities of trajectory behavior, etc. Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section “Investigation of functions and plot of their graphs” of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. In the present paper, we construct ensembles of trajectories in phase portraits of some dynamical systems. These ensembles are 2-dimensional surfaces invariant with respect to shifts along the trajectories. This is analogous to classical construction in analytic mechanics, i. e. the level surfaces of motion integrals (energy, kinetic moment, etc.). Such surfaces compose foliations in phase portraits of dynamical systems of Hamiltonian mechanics. In contrast with this classical mechanical case, the foliations considered in this paper have singularities: all their leaves have a non-empty intersection, they contain limit cycles on their boundaries. Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations

Energy input is primary controller of methane bubbling in subarctic lakes

Emission of methane (CH4) from surface waters is often dominated by ebullition (bubbling), a transport mode with high‐spatiotemporal variability. Based on new and extensive CH4 ebullition data, we demonstrate striking correlations (r2 between 0.92 and 0.997) when comparing seasonal bubble CH4 flux from three shallow subarctic lakes to four readily measurable proxies of incoming energy flux and daily flux magnitudes to surface sediment temperature (r2 between 0.86 and 0.94). Our results after continuous multiyear sampling suggest that CH4 ebullition is a predictable process, and that heat flux into the lakes is the dominant driver of gas production and release. Future changes in the energy received by lakes and ponds due to shorter ice‐covered seasons will predictably alter the ebullitive CH4 flux from freshwater systems across northern landscapes. This finding is critical for our understanding of the dynamics of radiatively important trace gas sources and associated climate feedback

Sub-Doppler Investigations of the Spectra of Molecules Isotopologues NH2D and HC3N

With the help of the sub-Doppler spectrometer created at IAP RAS, the spectra of molecules of once-deuterated ammonia NH2D, including 15NH2D, as well as 13C and 15N isotopologues of the molecule HC3N, were studied. Due to measurements based on the Lamb dip, the experimental accuracy of transition frequencies in the range of 85—503 GHz is improved by comparing conventional spectroscopyby approximately two orders of magnitude. The data obtained are of great interest both in studies of physical parameters in star-forming regions and in the search for possible variations of the fundamental constants. The molecule of partially deuterated ammonia NH2D is of particular interest because of the inversion-rotational transitions that lie in the mm spectral range and have different sensitivity to variations in the ratio of the electron mass to the proton mass.При помощи созданного в ИПФ РАН субдоплеровского спектрометра выполнены исследования спектров молекул NH2D, 15NH2D, а также 13C и 15N, изотопологов HC3N. Благодаря измерениям на основе провала Лэмба экспериментальные точности частот переходов в диапазоне 85 503 ГГц улучшены в сравнении с традиционной спектроскопией примерно на два порядка. Полученные данные представляют большой интерес при исследованиях физических параметров в областях звездообразования и при поиске возможных вариаций фундаментальных констант. Молекула NH2D представляет особый интерес из-за инверсионно-вращательных переходов, лежащих в миллиметровой области спектра и обладающих различной чувствительностью к вариации отношения массы электрона к массе протона.Все лабораторные измерения были выполнены благодаря поддержке РФФИ (проект № 16–02–00761). Анализ данных поддержан грантом РНФ (проект № 17–12–01256)