200 research outputs found
Reverse and dual Loomis-Whitney-type inequalities
Various results are proved giving lower bounds for the th intrinsic volume
, , of a compact convex set in , in
terms of the th intrinsic volumes of its projections on the coordinate
hyperplanes (or its intersections with the coordinate hyperplanes). The bounds
are sharp when and . These are reverse (or dual, respectively)
forms of the Loomis-Whitney inequality and versions of it that apply to
intrinsic volumes. For the intrinsic volume , which corresponds to mean
width, the inequality obtained confirms a conjecture of Betke and McMullen made
in 1983
Convergence in shape of Steiner symmetrizations
There are sequences of directions such that, given any compact set K in R^n,
the sequence of iterated Steiner symmetrals of K in these directions converges
to a ball. However examples show that Steiner symmetrization along a sequence
of directions whose differences are square summable does not generally
converge. (Note that this may happen even with sequences of directions which
are dense in S^{n-1}.) Here we show that such sequences converge in shape. The
limit need not be an ellipsoid or even a convex set.
We also deal with uniformly distributed sequences of directions, and with a
recent result of Klain on Steiner symmetrization along sequences chosen from a
finite set of directions.Comment: 11 page
Technical and Economic Overview of the Cellulignin Production Process
The paper analyses the chemical conversion process of biomass based on a diluted acid hydrolysis step, the Biomass Energy Process (BEM). The discussion starts from the technical point of view on the base of information reported literature, experimental laboratory analysis and pilot plant tests and then the authors tentatively explore the energy related costs of the process giving a comparison of the biomass derived solid fuel and fossil fuels. An evaluation of the product (cellulignin powder compacted into briquettes) and considered as a fuel and other energy source from ossil resources like oil, natural gas and coal, is reported considering the energy density and energy cost. The main technical feature of the process is the conversion of almost every type of bug wood biomass with large range of chemical and physics characteristics. The hydrolysis step determines the energy price and the threshold cost of the cellulignin is calculated at 60-70 euro/t about over which the NG energy is preferable. Environmental concerns can be however considered
Intersections of Dilatates of Convex Bodies
We initiate a systematic investigation into the nature of the function ∝K(L,ρ) that gives the volume of the intersection of one convex body K in Rn and a dilatate ρL of another convex body L in Rn, as well as the function ηK(L, ρ) that gives the (n - 1)-dimensional Hausdorff measure of the intersection of K and the boundary ∂(ρ L) of ρL. The focus is on the concavity properties of αK (L, ρ). Of particular interest is the case when K and L are symmetric with respect to the origin. In this situation, there is an interesting change in the concavity properties of αK (L, ρ) between dimension 2 and dimensions 3 or higher. When L is the unit ball, an important special case with connections to E. Lutwak\u27s dual Brunn-Minkowski theory, we prove that this change occurs between dimension 2 and dimensions 4 or higher, and conjecture that it occurs between dimension 3 and dimension 4. We also establish an isoperimetric inequality with equality condition for subsets of equatorial zones in the sphere S2, and apply this and the Brunn-Minkowski inequality in the sphere to obtain results related to this conjecture, as well as to the properties of a new type of symmetral of a convex body, which we call the equatorial symmetral
Convergence of symmetrization processes
Steiner and Schwarz symmetrizations, and their most important relatives, the
Minkowski, Minkowski-Blaschke, fiber, inner rotational, and outer rotational
symmetrizations, are investigated. The focus is on the convergence of
successive symmetrals with respect to a sequence of -dimensional subspaces
of . Such a sequence is called universal for a family of sets if
the successive symmetrals of any set in the family converge to a ball with
center at the origin. New universal sequences for the main symmetrizations, for
all valid dimensions of the subspaces, are found by combining two groups of
new results. In the first, a theorem of Klain for Steiner symmetrization is
extended to Schwarz, Minkowski, Minkowski-Blaschke, and fiber symmetrizations,
showing that if a sequence of subspaces is drawn from a finite set
of subspaces, the successive symmetrals of any compact convex
set converge to a compact convex set that is symmetric with respect to any
subspace in appearing infinitely often in the sequence. The
second group of results provides finite sets of subspaces such
that symmetry with respect to each subspace in implies full
rotational symmetry. It is also proved that for Steiner, Schwarz, and Minkowski
symmetrizations, a sequence of -dimensional subspaces is universal for the
class of compact sets if and only if it is universal for the class of compact
convex sets, and Klain's theorem is shown to hold for Schwarz symmetrization of
compact sets
Performance of electro-osmotic dewatering on different types of sewage sludge
The feasibility of pressure-driven electro-dewatering (EDW) on sludge samples taken after different biological
processes, stabilisation methods or mechanical dewatering techniques was assessed. First, the influence of
potential values on EDW of anaerobically and aerobically stabilised, mechanically dewatered, sludge samples
was investigated. Preliminary tests carried out by applying a constant potential (10, 15 and 20 V) in a lab-scale
device confirmed the possibility to reach a dry solid (DS) content of up to 42.9%, which corresponds to an
increase of 15% of the dry content in dewatered sludge without the application of the electrical field. Dewatering
increased with the applied potential but at the expense of a higher energy consumption. A potential equal to 15 V
was chosen as the best compromise for EDW performance, in terms of DS content and energy consumption. Then,
the influence of the mechanical dewatering was studied on aerobically stabilised sludge samples with a lower
initial DS content: the higher initial water content led to a lower final DS content but with a considerable
reduction of energy consumption. Finally, the biological process, studied by comparing sludge samples from
conventional activated sludge and membrane bioreactor processes, didn’t evidence any influence on EDW.
Experimental results shown that DS obtained after mechanical dewatering, volatile solids and conductivity are
the main factors influencing EDW. Anaerobically digested sludge reached the highest DS content, thanks to
lower organic fraction
Assessment of pressure-driven electro-dewatering as a single-stage treatment for stabilized sewage sludge.
- …