under favorable soil conditions such as existence of easily destructible organic compounds, balanced heat and moisture, adequate ventilation and abundant nutrients, organic materials are mineralized. once mineralizing occurs, mineral elements like p, s, ca, mg, k and other cations are released. a related study was conducted to determine the effect of seven organic fertilizers (leaf mold (lm), r...

Gold nanoparticles (NPs) were assembled and cross-linked into spherical aggregates by colloidal emulsion evaporation and ligand exchanging. The optical absorption, conventional transmission electron microscopy (TEM) and bright field (BF) TEM tomography confirm that the cross-linking of the pre-condensed aggregates generates high stability and compactness.

We study the subgroup structure of discrete groups which share cohomological properties which resemble non-negative curvature. Examples include all Gromov hyperbolic groups. A subgroup H ⊂ G is called s-normal, if H∩H is infinite for all g ∈ G. We provide strong restrictions on the possible s-normal subgroups of a Gromov hyperbolic group, or more generally a ’negatively curved’ group. Another r...

This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These GromovWitten type invariants depend on a Calabi-Yau A∞ category, which plays the role of the target in ordinary Gromov-Witten theory. When we use an appropriate A∞ version of the derived category of coherent sheaves on a Calabi-Yau variety, this constru...

We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n) time. It follows that the Gromo...

In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our theorems strengthen and gene...

This research announcement discusses our results on Gromov-Witten theory of root gerbes. A complete calculation of genus 0 Gromov-Witten theory of μr-root gerbes over a smooth base scheme is obtained by a direct analysis of virtual fundamental classes. Our result verifies the genus 0 part of the so-called decomposition conjecture which compares Gromov-Witten theory of étale gerbes with that of ...