Classes of submersions of Riemannian manifolds with compact fibers

In Riemannian geometry and its applications, the most popular is the class of Riemannian submersions (and foliations) [1–4] which are characterized by simplest mutual disposition of fibers. The purpose of the present article is to introduce other, more general, classes of submersions of Riemannian manifolds which, as well as the class of Riemannian submersions, are described by simple local properties of configuration tensors and to begin their study.Given a submersion :MM of differentiable manifolds with compact connected fibers and any metric onM, we define a metric on the base with the help of theL ²-norm of horizontal fields. In this caseT¯ M becomes a subbundle of some larger bundleM. The main class of totally geodesic submersions introduced in the article (Definition 1) corresponds to the metrics onM with simplest disposition ofT¯ M inM. In the article we obtain a criterion for such submersions (Corollary 1); existence is proved by means of the product with a metric varying along fibers (Example 2). To study totally geodesic submersions, we use ideas from the theory of Riemannian submersions and submanifolds with degenerate second form (Theorems 1 and 2 and Corollary 4).Foliations modeled by totally geodesic submersions (see equality (13)) are of interest too, but we leave them beyond the scope of the article.This work was supported by the Russian Foundation for Fundamental Research (Grant 94-01-00271).Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 1154–1164, September–October, 1994.     

Assessing the subsequent effect of nitrogen released from tobacco-waste on maize crop using a 15N isotope technique

The investigation of the residual effect of nitrogen (N) released from tobacco-waste (TW) using isotope techniques will provide valuable data for sustainable organic farming. For this aim, a pot experiment was conducted using the ¹⁵N isotope technique. The experiment was based on a completely randomised design with four replications and was conducted on a calcareous ustochrepts soil. TW at levels of 0, 10, 20, 30 and 40 t ha^?1 and N fertiliser as (NH₄)₂SO₄ at levels of 0, 20, 40, 60 and 80 kg N ha^?1 were used for the Bezostaja-1 wheat variety. Concerning mineral N fertilisation with 20 and 80 kg N ha^?1, additional treatments with ¹⁵N-labelled (NH₄)₂SO₂ (10 at.% exc.) have been applied. Following harvesting wheat plants, the Pioneer 3377 maize variety was used to see the residual effect of TW. After harvesting, dry matter yields were recorded and total N concentrations were determined. ¹⁵N determinations and calculations were also made for ¹⁵N treatments separately. TW had a significant residual effect on the growth of corn plant under the pot condition. Increasing rates of TW significantly increased the dry matter yield of corn plant following wheat from 3.31 t ha^?1 (at control) to 7.89 t ha^?1 (at the TW treatment of 40 t ha^?1). The ¹⁵N values derived from the ¹⁵N fertiliser decreased with increasing TW application. The average values of N derived from N fertiliser (Ndff) varied from 2.14 to 3.09% at the rates of 20 and 80 kg N ha^?1, respectively. However, N derived from TW (Ndftw) significantly increased from 16.93 to 24.59% (at 20 kg N ha^?1), and it also increased from 23.06 to 28.15% (at 80 kg N ha^?1) with increasing TW applications from 20 to 40 t ha^?1, respectively.     

Electron-beam poling in undoped, N- or Ge-doped MDECR H:SiO2 films

Amorphous N- or Ge-doped H:SiO₂ films deposited on silica by the matrix distributed electron cyclotron resonance-PECVD method were irradiated by an electron-beam with different doses in order to pole the material and induce second harmonic generation (SHG). SHG was measured using the Maker-fringe method. When irradiated at an acceleration voltage of 25 kV, an incident current of 5 nA during 480 s, the N-doped H:SiO₂ films exhibited a maximum second harmonic signal in the order of 0.003 pm/V, but when irradiated with an acceleration voltage of 30 kV, at 5 nA during 240 s, the films exhibited a maximum second harmonic signal of 0.006 pm/V. With a smaller current of 0.5 nA during 25 s and 25 kV acceleration voltage, the Ge-doped H:SiO₂ films (3.8 at. % Ge) showed a maximum second-order nonlinearity of 0.0005 pm/V. But an H:SiO₂ films with a smaller Ge content (1.0 at. % Ge), showed a large SHG: d₃₃=0.09 pm/V when irradiated at 25 kV, 0.5 nA during 15 s. PACS 78.66.J; 42.65.K; 68.60.D     

The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most O(Δ ⁵). In particular, we answer the question of Dujmovi? et al. (Comput Geom 38(3):194–212, 2007) whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(Δ) slopes.     

A Note on the Game Chromatic Index of Graphs

In this note we prove that the game chromatic index χ _g ^′(G) of a graph G of arboricity k is at most Δ + 3k − 1. This improves a bound obtained by Cai and Zhu [J. Graph Theory 36 (2001), 144–155] for k-degenerate graphs. Tomasz Bartnicki: Research of the first author is supported by a PhD grant from Polish Ministry of Science and Higher Education N201 2128 33. Received: November 1, 2006. Final version received: December 22, 2007.     

Separation of PCR-ready DNA from dairy products using magnetic hydrophilic microspheres and poly(ethylene glycol)-NaCl water solutions

Carboxyl group-containing magnetic nonporous poly(2-hydroxyethyl methacrylate-co-glycidyl methacrylate) (P(HEMA-co-GMA)) and magnetic glass microspheres were used for the isolation of bacterial DNA. P(HEMA-co-GMA) microspheres were prepared by the dispersion polymerization in toluene/2-methylpropan-1-ol mixture in the presence of magnetite nanoparticles obtained by coprecipitation of Fe(II) and Fe(III) salts with ammonium hydroxide. Carboxyl groups were then introduced by oxidation of the microspheres with potassium permanganate. The most extensive DNA recovery was achieved at PEG 6000 concentrations of 12% or 16% and 2 M NaCl. The method proposed was used for bacterial DNA isolation from different dairy products containing Bifidobacterium and Lactobacillus cells. The presence of target DNA and the quality of isolated DNA were checked by polymerase chain reaction (PCR) amplification with specific primers.     

Partitioning 2-edge-colored graphs by monochromatic paths and cycles

We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the vertex set of every 2-edge-colored graph can be partitioned into at most 2α(G) monochromatic cycles, where α(G) denotes the independence number of G. Another direction, emerged recently from a conjecture of Schelp, is to consider colorings of graphs with given minimum degree. We prove that apart from o(|V (G)|) vertices, the vertex set of any 2-edge-colored graph G with minimum degree at least \(\tfrac{{(1 + \varepsilon )3|V(G)|}} {4}\) can be covered by the vertices of two vertex disjoint monochromatic cycles of distinct colors. Finally, under the assumption that \(\bar G\) does not contain a fixed bipartite graph H, we show that in every 2-edge-coloring of G, |V (G)| ? c(H) vertices can be covered by two vertex disjoint paths of different colors, where c(H) is a constant depending only on H. In particular, we prove that c(C ₄)=1, which is best possible.     

Backscattering suppression in supersonic 1D polariton condensates

We investigate the effect of disorder on the propagation of one-dimensional polariton condensates in semiconductor microcavities. We observe a strong suppression of the backscattering produced by the imperfections of the structure when increasing the condensate density. This suppression occurs in the supersonic regime and is simultaneous to the onset of parametric instabilities which enable the "hopping" of the condensate through the disorder. Our results evidence a new mechanism for the strong scattering reduction of polaritons at high speeds.