Ramseyan variations on symmetric subsequences

A theorem of Dekking in the combinatorics of words implies that there exists an injective order-preserving transformation f : {0, 1, . . . , n} → {0, 1, . . . , 2n} with the restriction f(i + 1) ≤ f(i) + 2 such that for every 5-term arithmetic progression P its image f(P) is not an arithmetic progression. In this paper we consider symmetric sets in place of arithmetic progressions and prove lower and upper bounds for the maximum M = M(n) such that every f as above preserves the symmetry of at least one symmetric set S ⊆ {0, 1, . . . , n} with |S| ≥ M

Structural properties of extremal asymmetric colorings

Let Ω be a space with probability measure µ for which the notion of symmetry is defined. Given A ⊆ Ω, let ms(A) denote the supremum of µ(B) over symmetric B ⊆ A. An r-coloring of Ω is a measurable map χ : Ω → {1, . . . , r} possibly undefined on a set of measure 0. Given an r-coloring χ, let ms(Ω; χ) = max₁≤i≤r ms(χ⁻¹ (i)). With each space Ω we associate a Ramsey type number ms(Ω, r) = infχ ms(Ω; χ). We call a coloring χ congruent if the monochromatic classes χ⁻¹ (1), . . . , χ⁻¹ (r) are pairwise congruent, i.e., can be mapped onto each other by a symmetry of Ω. We define ms* (Ω, r) to be the infimum of ms(Ω; χ) over congruent χ. We prove that ms(S¹ , r) = ms* ([0, 1), r) for the unitary interval of reals considered with central symmetry, and explore some other regularity properties of extremal colorings for various spaces

Untangling polygons and graphs

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at least \Omega(n^{2/3}) vertices fixed. For any graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.Comment: 11 pages, 3 figure

A polynomial bound for untangling geometric planar graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos [Discrete Comput. Geom., 2002] asked if every n-vertex geometric planar graph can be untangled while keeping at least n^\epsilon vertices fixed. We answer this question in the affirmative with \epsilon=1/4. The previous best known bound was \Omega((\log n / \log\log n)^{1/2}). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least (n/3)^{1/2} vertices fixed, while the best upper bound was O(n\log n)^{2/3}. We answer a question of Spillner and Wolff [arXiv:0709.0170 2007] by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than 3(n^{1/2}-1) vertices fixed. Moreover, we improve the lower bound to (n/2)^{1/2}.Comment: 14 pages, 7 figure

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Photoluminescence of melanin-based nanocomposites with fullerene derivative

This paper presents the study of the photoluminescent properties of molecular compositions consisting of melanin and an electron-acceptor material – fullerene derivative, [6,6]-phenyl C61 butyric acid methyl ester (PCBM). These molecular compositions have not been studied well and are promising for molecular electronics of natural materials, in particular, for organic solar cells. The novelty of this work relates to the study of photoluminescence spectra obtained for these molecular compositions and nanocomposites in various solvents (chloroform, acetonitrile, and toluene) as well as in a polystyrene matrix; these studies were carried out at various, in particular, liquid helium (4.2 K), temperatures. The obtained results allowed us to ascertain mechanisms of the state of aggregation and donor-acceptor interaction between melanin and PCBM

STUDY OF SENSORS FOR DETECTING EXPLOSIVE SUBSTANCES

Results of the study of sensitivity of fluorescent сhemosensory substances to impact of nitroaromatic explosives and synthesis methods are described

DEVICE FOR NITROAROMATIC SUBSTANCE DETECTING AND IDENTIFICATION

Designing and modeling of optic-related part of device for nitroaromatic substance detection are described

Результаты интрагастральной рН-метрии у пострадавших с обширными ожогами

Aim of study To study of the role of hydrochloric acid in the genesis of stress-induced gastric ulceration in patients with extensive burns.Material and methods The results of gastroscopy and endoscopic pH-metry of 30 young patients with extensive burns (19 male patients and 11 female patients). The acidity of the gastric contents was measured on day 1,7 and 14 after the trauma.Results It was found that the early period of burn disease was followed by the pH growth in the acid-producing area of the stomach to 3.8–4.2 (p=0.002–0.020). This indicated that extensive burns provoked a significant decrease of  hydrochloric acid production by parietal cells of the stomach. The restoration of the acid production occurred only 14 days after thermal injury and was not followed by the development of a hyperacid state. The frequency of erosive-ulcerative lesions detection in the gastric mucosa by the end of the first day after receiving burns was 83%, 87% on day 7, and 96% on day 14. In total, stress-induced lesions of the gastrointestinal mucosa were diagnosed in 26 of 30 patients with a shock-induced thermal injury. Consequently, in patients with burn shock the protective factors of the gastric mucosa were depressed so that a minimum amount of hydrochloric acid was sufficient to damage it.Conclusion Inhibition of acidogenic function is typical for patients with burn disease. Hydrochloric acid does not play a leading role in the genesis of stressinduced ulceration in patients with severe thermal trauma.Цель исследования Изучение роли соляной кислоты в генезе эрозивно-язвенных поражений слизистой оболочки пищеварительного тракта у пострадавших с обширными ожогами.Материал и методы Представлены результаты обследования 30 пациентов с тяжелой термической травмой. Для оценки морфологических изменений слизистой оболочки выполняли эндоскопическое исследование желудка и двенадцатиперстной кишки (ДПК), кислотопродуцирующую функцию желудка исследовали методом эндоскопической рН-метрии.Результаты Ранний период ожоговой болезни сопровождается подавлением кислотообразующей функции (pH 3,8–4,2) и субкомпенсацией ощелачивающей функции (pH 2,8–4,8) желудка. Восстановление достаточной продукции соляной кислоты происходит не ранее 14-х сут от момента термической травмы. Однако, несмотря на значительное снижение дебита хлористоводородной кислоты, стресс-индуцированные повреждения слизистой оболочки желудочно-кишечного тракта диагностированы у 86% пострадавших с шокогенной термической травмой. Полученные данные свидетельствуют о том, что в условиях ожогового шока факторы защиты слизистой оболочки желудка угнетаются настолько, что для ее повреждения достаточно минимального количества соляной кислоты.Вывод Угнетение кислотопродуцирующей функции желудка характерно для раннего периода ожоговой болезни. Соляная кислота не играет ведущей роли в генезе стресс-индуцированных поражений желудка и ДПК у пациентов с тяжелой термической  травмой