Cutting the same fraction of several measures

We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure

Graphene as a quantum surface with curvature-strain preserving dynamics

We discuss how the curvature and the strain density of the atomic lattice generate the quantization of graphene sheets as well as the dynamics of geometric quasiparticles propagating along the constant curvature/strain levels. The internal kinetic momentum of Riemannian oriented surface (a vector field preserving the Gaussian curvature and the area) is determined.Comment: 13p, minor correction

Cohomologies of the Poisson superalgebra

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket for arbitrary n>0. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys. supplemented by computation of the 3-rd trivial cohomolog

Cotangent bundle quantization: Entangling of metric and magnetic field

For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an irreducible representation of this algebra in $L^2(\cal M)$. This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions this algebra is unique. The non-commutative product over $T^*\cal M$ is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals this product has a front, which is described in terms of geodesic triangles in $\cal M$. The quantization of $\delta$-functions induces a family of symplectic reflections in $T^*\cal M$ and generates a magneto-geodesic connection $\Gamma$ on $T^*\cal M$. This symplectic connection entangles, on the phase space level, the original affine structure on $\cal M$ and the magnetic field. In the classical approximation, the $\hbar^2$-part of the quantum product contains the Ricci curvature of $\Gamma$ and a magneto-geodesic coupling tensor.Comment: Latex, 38 pages, 5 figures, minor correction

Study of the Fast X-Ray Transient XTE J1901+014 Based on INTEGRAL, RXTE and ROSAT Data

The source XTE J1901+014 discovered by the RXTE observatory during an intense outburst of hard radiation and classified as a fast X-ray transient is studied. The source's spectral characteristics in the quiescent state have been investigated for the first time both in the soft X-ray energy range (0.6-20 keV) based on ROSAT and RXTE data and in the hard energy range (>20 keV) based on INTEGRAL data. A timing analysis of the source's properties has revealed weak nonperiodic bursts of activity on time scales of several tens of seconds and two intense ($\sim$0.5-1 Crab) outbursts more than several hundred seconds in duration. Certain assumptions about the nature of the object under study are made.Comment: 19 pages, 7 figure

Degenerate Odd Poisson Bracket on Grassmann Variables

A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $\Delta$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $\Delta$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.Comment: 5 pages, LATEX. Corrections of misprints. The relation (23) is adde

The Lie algebroid Poisson sigma model

The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory and the gauged A topological sigma model. In this paper, generalizing the above construction, we construct the Lie algebroid Poisson sigma model. This is yielded by gauging a Hamiltonian Lie groupoid symmetry of the Poisson sigma model target space. We use the BV quantization approach in the AKSZ geometrical version to ensure consistent quantization and target space covariance. The model has an extremely rich geometry and an intricate BV cohomology, which are studied in detail.Comment: 52 pages, Late

Assessing Potato Psyllid Haplotypes in Potato Crops in the Pacific Northwestern United States

The potato psyllid, Bactericera cockerelli (Šulc), is a vector of the bacterium ‘Candidatus Liberibacter solanacearum’ (Lso) that has been linked to the economically devastating zebra chip disease of potato. To date, four haplotypes of the potato psyllid have been identified and include Central, Western, Northwestern, and Southwestern haplotypes. Zebra chip was reported in potato crops in the Pacific Northwestern United States for the first time in 2011, and the Lso-infected psyllids collected from zebra chip-affected fields were identified as the Western haplotype. Additional studies have reported a mix of the Western and Northwestern psyllid haplotypes in the Pacific Northwest. The present study further examined psyllid population dynamics over the duration of the 2012 potato season in the Pacific Northwest by haplotype analysis of 864 potato psyllids collected from potato fields in Washington, Oregon, and Idaho. In the Yakima Valley of Washington and the lower Columbia Basin of Washington and Oregon, the Northwestern haplotype was predominant (78%), and was detected earlier in the season than the Western haplotype. Interestingly, in south-central Idaho, all four psyllid haplotypes were identified, but the predominant haplotype was the Western haplotype (77%). Here, Northwestern psyllids were detected early in the season from June to mid-August, whereas Central psyllidswere detected in late July and thereafter. These results suggest that haplotype composition of psyllid populations in potato fields throughout the 2012 growing season in south-central Idaho differed greatly from those in Washington and Oregon. Additionally, all psyllids were analyzed for the presence of Lso, and no Lso-positive psyllids were found in Washington and Oregon, whereas Lso-positive psyllids were found in south-central Idaho. These Lso-positive psyllids consisted of the Western, Northwestern, and Central haplotypes

Клинико-эпидемиологические особенности менингококковой инфекции у детей в период спорадической заболеваемости

Purpose: to evaluate epidemiologic situation as to meningococcal infection and reveal clinical-epidemiological features of the disease on the territory of Krasnoyarsk сity and Krasnoyarsk Krai at the present stage. Data and methods: The research gives the analysis of MI morbidity and mortality rates in children of the region according to official information from the Federal Service for Supervision of Consumer Rights Protection and Human Welfare in Krasnoyarsk Krai for the period 2000–2014. The work studies clinical and epidemiological features of the disease in 53 patients with the generalized form of meningococcal infection (GFMI) who were treated in the infectious disease department of the Regional Interdistrict Children’s Clinical Hospital of Krasnoyarsk for the period 2010–2014. Results: The epidemiological situation as to MI in Krasnoyarsk for the period 2000-2013 years is characterized by the signs of interepidemic period with morbidity rises in the winter-spring period. Children from 1 year to 3 years (54,7%) prevail over all MI diseased. The number of children in the first year of life decreased almost two times (from 40% to 20,7%). At the same time the proportion of children older than 4 years increased. The leading serotype among laboratory-confirmed cases of MI in Krasnoyarsk Krai is still the B group meningitis (64,7%). Conclusion: On the territory of Krasnoyarsk Krai the MI morbidity is sporadic. The generalized forms of meningococcal infection are characterized by early overt symptoms which make it possible to set a diagnosis. The clinical picture of the generalized forms of the disease almost did not change significantly. Цель: оценить эпидемическую ситуацию по МИ и выявить клинико-эпидемиологические особенности заболевания на территории г. Красноярска и Красноярского края на современном этапе. Материалы и методы: проведен анализ показателей заболеваемости и летальности от МИ у детей региона согласно официальным данным Управления Федеральной службы по надзору в сфере защиты прав потребителей и благополучия человека по Красноярскому краю за период 2000–2014 гг. Изучены клинико-эпидемиологические особенности заболевания у 53 больных ГФМИ, находившихся на лечении в инфекционном отделении Краевой межрайонной детской клинической больницы г. Красноярска за период 2010–2014 гг. Результаты: Эпидемическая ситуация по МИ в г. Красноярске за период 2000–2014 гг. характеризуется признаками межэпидемического периода с подъемами заболеваемости в зимне-весенний период. Среди заболевших МИ преобладают дети в возрасте от 1 до 3 лет (54,7%), почти в 2 раза (с 40% до 20,7%) уменьшилось количество детей первого года жизни, в то же время увеличился удельный вес детей старше 4 лет. Лидирующим серотипом среди лабораторно подтвержденных случаев МИ в Красноярском крае по-прежнему является менингококк группы В (64,7%). Заключение: на территории Красноярского края заболеваемость менингококковой инфекцией носит спорадический характер. При генерализованных формах менингококковой инфекции рано появляются характерные манифестные симптомы, наличие которых позволяет поставить диагноз, клиническая картина генерализованных форм заболевания практически не претерпела существенных изменений.