157 research outputs found
Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling
A distance labeling scheme is an assignment of bit-labels to the vertices of
an undirected, unweighted graph such that the distance between any pair of
vertices can be decoded solely from their labels. An important class of
distance labeling schemes is that of hub labelings, where a node
stores its distance to the so-called hubs , chosen so that for
any there is belonging to some shortest
path. Notice that for most existing graph classes, the best distance labelling
constructions existing use at some point a hub labeling scheme at least as a
key building block. Our interest lies in hub labelings of sparse graphs, i.e.,
those with , for which we show a lowerbound of
for the average size of the hubsets.
Additionally, we show a hub-labeling construction for sparse graphs of average
size for some , where is the
so-called Ruzsa-Szemer{\'e}di function, linked to structure of induced
matchings in dense graphs. This implies that further improving the lower bound
on hub labeling size to would require a
breakthrough in the study of lower bounds on , which have resisted
substantial improvement in the last 70 years. For general distance labeling of
sparse graphs, we show a lowerbound of , where is the communication complexity of the
Sum-Index problem over . Our results suggest that the best achievable
hub-label size and distance-label size in sparse graphs may be
for some
Cokebildung und Entcoking während der Methanbildung und des Methanzerfalls auf Ni-Cu-Trägerkatalysatoren
The effect of the composition of silica supported Ni-Cu alloy
catalysts on the process of coking and decoking during methane
decomposition and during methanation was considered. The kinetics
of methanation was studied and compared to those of carbon
deposition and of strong adsorption of hydrogen. Initiation of the
formation of filamentous carbon formation on mono-metallic surfaces
may take place if the ratio of the partial pressures, pCO/pH2, is
larger than 2 (T 673 K). Once the process starts,
the chemical potential of the gas phase may be reduced to lower
values without interruption of filament growth. Besides, it was concluded
that the methanation reaction includes two steps: the dissociative
adsorption of CO and the hydrogenation of the adsorbed
species. It was possible to establish the mechanism through which
Cu affects the activity of Ni. The effect of the composition of the
alloy catalysts on the methane formation and on the simultaneous
carbon deposition indicates that those reactions belong to group I
and to group II, respectively, following Ponec's classification. It
was possible to find the optimal Cu concentration that maximises
methanation and minimises carbon deposition. The kinetics of
methane decomposition was also considered and is well described
by adapting a model developed by other authors for Fe catalysts
A simpler and more efficient algorithm for the next-to-shortest path problem
Given an undirected graph with positive edge lengths and two
vertices and , the next-to-shortest path problem is to find an -path
which length is minimum amongst all -paths strictly longer than the
shortest path length. In this paper we show that the problem can be solved in
linear time if the distances from and to all other vertices are given.
Particularly our new algorithm runs in time for general
graphs, which improves the previous result of time for sparse
graphs, and takes only linear time for unweighted graphs, planar graphs, and
graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201
Kohlenstoffbildung auf Nickel und Nickel-Kupfer-Legierungskatalysatoren
Equilibrium, kinetic and morphological studies of carbon formation
in CH4+H2, CO, and CO+H2 gases on silica supported nickel
and nickel-copper catalysts are reviewed. The equilibrium deviates
in all cases from graphite equilibrium and more so in CO+CO2
than in CH4+H2. A kinetic model based on information from surface
science results with chemisorption of CH4 and possibly also
the first dehydrogenation step as rate controlling describes carbon
formation on nickel catalyst in CH4+H2 well. The kinetics of
carbon formation in CO and CO+H2 gases are in agreement
with CO disproportionation as rate determining step. The presence
of hydrogen influences strongly the chemisorption of CO. Carbon
filaments are formed when hydrogen is present in the gas while
encapsulating carbon dominates in pure CO. Small amounts of
Cu alloying promotes while larger amounts (Cu : Ni ≥ 0.1) inhibits
carbon formation and changes the morphology of the filaments
("octopus" carbon formation). Adsorption induced nickel segregation
changes the kinetics of the alloy catalysts at high carbon activities.
Modifications suggested in some very recent papers on the
basis of new results are also briefly discussed.Center for Surface Reactivity
Bioaccumulation and ecotoxicity of carbon nanotubes
Carbon nanotubes (CNT) have numerous industrial applications and may be released to the environment. In the aquatic environment, pristine or functionalized CNT have different dispersion behavior, potentially leading to different risks of exposure along the water column. Data included in this review indicate that CNT do not cross biological barriers readily. When internalized, only a minimal fraction of CNT translocate into organism body compartments. The reported CNT toxicity depends on exposure conditions, model organism, CNT-type, dispersion state and concentration. In the ecotoxicological tests, the aquatic organisms were generally found to be more sensitive than terrestrial organisms. Invertebrates were more sensitive than vertebrates. Single-walled CNT were found to be more toxic than double-/multi-walled CNT. Generally, the effect concentrations documented in literature were above current modeled average environmental concentrations. Measurement data are needed for estimation of environmental no-effect concentrations. Future studies with benchmark materials are needed to generate comparable results. Studies have to include better characterization of the starting materials, of the dispersions and of the biological fate, to obtain better knowledge of the exposure/effect relationships
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