Analogues of the central point theorem for families with dd-intersection property in Rd\mathbb R^d

In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families

DUST PARTICLE CHARGE DETERMINATION IN CONSIDERATION OF NON-LOCAL EFFECTS IN A STRATIFIED GLOW DISCHARGE

A new theoretical method of dust particle charge determination is provided. This method is based on the calculation of the ion and electron fluxes on the dust particle surface in a spatially periodic strata field. The electron flux is calculated through the non-local electron distribution function (EDF), which is formed by inhomogeneous strata potential. The comparison between proposed theoretical method and the traditional method of using Maxwell EDF for dust particle charge calculation is done87-8

Fractional Derivative as Fractional Power of Derivative

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.Comment: 20 pages, LaTe

Phase Splitting for Periodic Lie Systems

In the context of the Floquet theory, using a variation of parameter argument, we show that the logarithm of the monodromy of a real periodic Lie system with appropriate properties admits a splitting into two parts, called dynamic and geometric phases. The dynamic phase is intrinsic and linked to the Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric phase is represented as a surface integral of the symplectic form of a co-adjoint orbit.Comment: (v1) 15 pages. (v2) 16 pages. Some typos corrected. References and further comments added. Final version to appear in J. Phys. A

Tur\'an numbers for Ks,tK_{s,t}-free graphs: topological obstructions and algebraic constructions

We show that every hypersurface in $\R^s\times \R^s$ contains a large grid, i.e., the set of the form $S\times T$, with $S,T\subset \R^s$. We use this to deduce that the known constructions of extremal $K_{2,2}$-free and $K_{3,3}$-free graphs cannot be generalized to a similar construction of $K_{s,s}$-free graphs for any $s\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.Comment: Fixed a small mistake in the application of Proposition

Клинико-эпидемиологические аспекты коклюша у детей в условиях массовой вакцинопрофилактики

The aim of the study was to present clinical, epidemiological and laboratory characteristics of modern pertussis in hospitalized children, as well as to assess the frequency of pertussis infection as an etiological factor of long – term cough in children and adolescents.Materials and methods: medical records of 545 patients hospitalized in Children’s city clinical hospital №5 named after N.F. Filatov (Saint-Petersburg) in the period 2015–2017 were analyzed. Detailed clinical and laboratory analysis with subsequent follow-up of patients was carried out in 80 patients with pertussis aged 1 month to 18 years. The DNA of the causative agents of pertussis infection was identified by PCR using a commercial kit “AmpliSens Bordetella multi-FL” (Moscow); parallel was determined the bacterial load by quantitative PCRRT (real time) using test systems production, Gamaleya Research Institute of Epidemiology and Microbiology (Moscow), allowing to detect a single genome-equivalents (GE) of B. pertussis in smears from the nasopharynx. Pertussis convalescents were examined 1, 3 and 6 months after discharge.Results. Among hospitalized children dominated the first 2 years of life (70.8%), 78% were unvaccinated children. The sources of infection for children of the first two years of life were family members in 77% of cases, for preschoolers-in 67%, for schoolchildren-in 14%. Patients of moderate severity were 81.1%, severe – 10.3%; mild – 7%. Of the specific complications, respiratory rhythm disturbances were notedin 11.6%, including respiratory arrest-in 2.8%; pneumonia of mixed etiology was recorded in 6.2% of cases. Introduction of PCR method allows to increase laboratory confirmation up to 87.2%. In 63.6% of cases pertussis of pertussis were detected by PCR genome-equivalents of DNA in 6 months from hospital discharge. In patients with long – term cough, pertussis wand DNA was detected in preschool children in 11.14% of cases, in patients 7–12 years – in 25.93%, in adolescents-in 20% of cases.Conclusion. Whooping cough is a common infection among schoolchildren and adolescents, despite the high coverage of young children with preventive vaccinations. Pertussis convalescents can release the DNA of the pathogen for a long time, which may have epidemiological significance for unvaccinated and those children and adults, who have lost postvaccinal immunity, in the foci of infection.Цель: представить клинико-эпидемиологические и лабораторные характеристики современного коклюша у госпитализированных детей, а также оценить частоту коклюшной инфекции как этиологического фактора длительного кашля у детей и подростков.Материалы и методы: проанализированы медицинские карты 545 стационарных больных, госпитализированных в ДГКБ № 5 им. Н.Ф. Филатова (СанктПетербург) в период 2015–2017 гг. Детальный клинико-лабораторный анализ с последующим динамическим наблюдением реконвалесцентов проводили у 80 больных коклюшем в возрасте от 1 месяца до 18 лет. ДНК возбудителей коклюшной инфекции выделяли методом ПЦР с использованием коммерческого набора «АмплиСенс ®Bordetella multi-FL» (Москва); параллельно определяли бактериальную нагрузку методом количественного ПЦР-РТ (real time) с помощью тест-системы производства ФНИЦЭМ им. Н.Ф. Гамалеи МЗ РФ (Москва), позволяющей обнаруживать единичные геном-эквиваленты (ГЭ) B. pertussis в мазках из носоглотки. Реконвалесценты коклюша обследованы через 1, 3 и 6 месяцев после выписки.Результаты: среди госпитализированных преобладали дети первых 2 лет жизни (70,8%), 78% составляли непривитые дети. Источниками инфекции для детей первых двух лет жизни были члены семьи в 77% случаев, для дошкольников – в 67%, для школьников – в 14%. Пациенты средней степени тяжести составили 81,1%, тяжелой – 10,3%; легкой – 7%. Из специфических осложнений отмечали нарушения ритма дыхания – в 11,6%, в том числе остановки дыхания – в 2,8%; пневмонии смешанной этиологии регистрировали в 6,2% случаев. Внедрение метода ПЦР позволяет повысить лабораторное подтверждение до 87,2%. У реконвалесцентов коклюша до 6 месяцев от выписки из стационара в 63,6% случаев методом ПЦР-РВ выявлялись геном-эквиваленты ДНК B.Pertussis. У пациентов с длительным кашлем ДНК коклюшной палочки выявляли у дошкольников в 11,14% случаев, у пациентов 7–12 лет – в 25,93%, у подростков – в 20% случаев.Заключение. Коклюш является распространенной инфекцией среди школьников и подростков, несмотря на высокий охват детей раннего возраста профилактическими прививками. Реконвалесценты коклюша могут длительно выделять ДНК возбудителя, что может иметь эпидемиологическое значение для непривитых и утративших поствакцинальный иммунитет детей и взрослых в очагах инфекции

3D model and prototype of circulating fluidiezed bed boiler

Creation of a 3D model of a boiler with a circulating fluidized bed according to the surviving drawings. Optimization of the developed assembly for printing on a 3D printer. Creation and pasting of the physical model of the boiler for placement in the nominal audience of Professor A.P. Baskakov.Создание функциональной 3D модели котла с циркулирующим кипящим слоем смонтированного в проблемной лаборатории УрФУ по сохранившимся чертежам, для проведения численных исследований. Оптимизация разработанной сборки для печати на 3D принтере. Создание и склейка физического макета котла для размещения в именной аудитории профессора А.П. Баскакова