Determination of microelement distribution in different components of soil-plant systems

The leaves, stem, and roots of two types of shrubs (tea (Camellia sinensis) and sweet leaf (Sauropus androgynus)) and two types of herbs (vetiver grass (Vetiveria zizanioides L. Nash) and maize (Zea mays L)) and the Thucuc soil where the plants were growing were collected to be studied. The contents of 22 elements in the samples were determined by three methods: X-Ray fluorescence analysis (XRFA), gamma activation analysis (GAA), and the tracking method to study the distribution of these elements in plants and the soil-plant relationship. This study was carried out at the Flerov Laboratory of Nuclear Reactions (FLNR), Joint Institute for Nuclear Research (JINR), Dubna, Russia. The distribution of the elements in the soil-plant system was studied.     

Computing material collapse displacement fields on a cray X-MP/48 by the LP primal affine scaling algorithm

A pair of dual, highly degenerate linear programs modeling the static and kinematic principles of limit analysis are studied. They arise from mixed finite element discretizations of the continuous saddle point problem and piecewise linear approximations of the convex unbounded Mises set of admissible stresses. We use piecewise constant stresses and piecewise bilinear displacements, and present computational results with the Affine Scaling Algorithm a la Dikin (1967) and Karmarker (1984). Graphical displays are presented for material collapse fields of a rectangular solid with thin cuts under tension, in problem sizes up to 9000 variables and 7700 equations. To our knowledge, these stress fields have not been computed before.The research underlying this report was supported by NSF Grants ECS-8500940 at Carnegie-Mellon University and the University of Iowa and by ECS-8696087 at the University of Iowa. A preliminary version of this paper was presented at the Supercomputers and Large-Scale Optimization Workshop at the University of Minnesota, Minneapolis, May 16–18, 1988.     

Harmonic functions of polynomial growth on certain complete manifolds

Given a complete manifold with a particular structure at infinity, we give the dimension of the space of harmonic functions with prescribed polynomial growth.     

Growth peculiarities during vapor–liquid–solid growth of silicon nanowhiskers by electron-beam evaporation

One-dimensional (1D) silicon (Si) nanostructures were grown by electron-beam evaporation catalyzed by gold nanoparticles on silicon substrates following the vapor–liquid–solid growth mechanism. We report three strikingly different growth morphologies of the 1D Si nanostructures and discuss their formation. The morphology of the silicon nanostructures strongly depends on gold layer thickness, annealing temperature before deposition and growth temperature during the deposition. The formation of nanoscale silicon features such as nanobelts, nanowires and nanowhiskers was observed. The nanoscale silicon features were characterized by transmission and scanning electron microscopy using imaging, diffraction and energy-dispersive X-ray spectroscopy, atomic force microscopy and UV micro-Raman spectroscopy. PACS 68.37.Lp; 68.70.+w; 78.30.-j; 81.15.Jj     

Scattering theory for perturbed stratified media

We study the operatorH = -c ² x,y)Μx,y)∇ · Μ ^-1 (x,y)∇, wherec andΜ are perturbations of functionsc ₀(y) andΜ ₀(y) which depend only on the one-dimensional variabley. In particular, we study the spatial asymptotics of lim_ε↺0(H - (λ +iε)²)^-1 applied to functions which have compact support or are otherwise well-behaved at infinity and relate the scattering matrix to the asymptotics of the generalized eigenfunctions. We then prove a trace formula for the operatorH in terms of the scattering phase, and, in a very special situation, use the trace formula to find spectral asymptotics forH. Partially supported by an NSF Postdoctoral Fellowship and the University of Missouri Research Board.     

Some Upper Bounds on the Number of Resonances for Manifolds with Infinite Cylindrical Ends

We prove some sharp upper bounds on the number of resonances associated with the Laplacian, or Laplacian plus potential, on a manifold with infinite cylindrical ends.     

Spectroscopic and structural characterization of pure and FeCl<Subscript>3</Subscript>-containing tri-<Emphasis Type="Italic">n</Emphasis>-butyl phosphate

The spectroscopic properties and liquid structure of pure tri-n-butyl phosphate (TBP) and FeCl₃/TBP solutions have been investigated by Uv–Vis and Raman spectroscopies, X-ray diffraction and conductometry. Uv–Vis and Raman spectra, supported by conductometric measurements, consistently indicate that the solubilized salt is present mostly as TBP _n [FeCl_3???n ] ⁿ⁺ and FeCl₄ ^? complex ions due to specific interaction with the TBP phosphate group. Thanks to this interaction, a high amount of salt (up to 13 % w/w) can be dissolved despite the relatively low dielectric constant of TBP. The X-ray diffractogram of pure TBP has been interpreted in terms of three main contributions which can be attributed to spatial pair correlations between atoms of interacting TBP molecules. In the presence of increasing FeCl₃ amounts, it has been observed a progressive structuring effect, exerted by the dissolved salt, on the layers of opportunely oriented TBP molecules due to the formation of the complex ionic species. By simple treatment with NaBH₄, the synthesis of Fe nanoparticles has been achieved. The absence of water, the easiness of preparation, the high amount of salt which can be suspended and the peculiar physico-chemical properties of such systems are all elements worth of note for the fields of nanoparticle synthesis and for specialized technological applications.     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].