424 research outputs found
Interstitial compounds as fuel cell catalysts - Their preparative techniques and electrochemical testing
Preparation and electrochemical testing methods for fuel cell catalysts using interstitial compound
Development of an improved oxygen electrode for use in alkaline H2-O2 fuel cells Quarterly report, Oct. 1 - Dec. 31, 1966
Interstitial compounds of transition elements prepared for improving oxygen electrode in alkaline hydrox fuel cel
Development of an improved oxygen electrode for use in alkaline H2-O2 fuel cells Quarterly report, Apr. 1 - Jun. 30, 1967
Preparation of institial compounds of transition metals for hydrogen oxygen fuel cell cathode
Изучение структуры цинктитановых боросиликатных стекол по данным рассеяния рентгеновских лучей под малыми углами
В статті вивчено мікронеоднорідну будову цинктитанових боросилікатних стекол та процесів фазового розділу в них за даним розсіяння нейтронів під малими кутами. Зроблено висновок про характер розподілення часток, що виділяються за розмірами, які змінюються в дослідних стеклах в залежності від вмісту в них TiO₂ та ZnO. Встановлено вплив наявності мікронеоднорідностей після варки на характер їх фазовогорозподілення.In paper the micronon-uniform structure zinc-titanium borosilicate glass and processes of phase separation in them according to diffusing under vanishing angles of neutrons is investigated. It is drawn a In paper the micronon-uniform structure zinc-titanium borosilicate glass and processes of phase separation in them according to diffusing under vanishing angles of neutrons is investigated. It is drawn a leading-out on distribution of depositing corpuscles character on sizes which changes in studied glasses depending on the contents in them TiO₂ and ZnO. Effect of presence micro micronon-uniforms after melting on character of their phase separationis established
The Complexity of Drawing Graphs on Few Lines and Few Planes
It is well known that any graph admits a crossing-free straight-line drawing
in and that any planar graph admits the same even in
. For a graph and , let denote
the minimum number of lines in that together can cover all edges
of a drawing of . For , must be planar. We investigate the
complexity of computing these parameters and obtain the following hardness and
algorithmic results.
- For , we prove that deciding whether for a
given graph and integer is -complete.
- Since , deciding is NP-hard for . On the positive side, we show that the problem
is fixed-parameter tractable with respect to .
- Since , both and
are computable in polynomial space. On the negative side, we show
that drawings that are optimal with respect to or
sometimes require irrational coordinates.
- Let be the minimum number of planes in needed
to cover a straight-line drawing of a graph . We prove that deciding whether
is NP-hard for any fixed . Hence, the problem is
not fixed-parameter tractable with respect to unless
Recognizing hyperelliptic graphs in polynomial time
Recently, a new set of multigraph parameters was defined, called
"gonalities". Gonality bears some similarity to treewidth, and is a relevant
graph parameter for problems in number theory and multigraph algorithms.
Multigraphs of gonality 1 are trees. We consider so-called "hyperelliptic
graphs" (multigraphs of gonality 2) and provide a safe and complete sets of
reduction rules for such multigraphs, showing that for three of the flavors of
gonality, we can recognize hyperelliptic graphs in O(n log n+m) time, where n
is the number of vertices and m the number of edges of the multigraph.Comment: 33 pages, 8 figure
A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs
We give an approximation algorithm for packing and covering linear programs
(linear programs with non-negative coefficients). Given a constraint matrix
with n non-zeros, r rows, and c columns, the algorithm computes feasible primal
and dual solutions whose costs are within a factor of 1+eps of the optimal cost
in time O((r+c)log(n)/eps^2 + n).Comment: corrected version of FOCS 2007 paper: 10.1109/FOCS.2007.62. Accepted
to Algorithmica, 201
A Unifying Model of Genome Evolution Under Parsimony
We present a data structure called a history graph that offers a practical
basis for the analysis of genome evolution. It conceptually simplifies the
study of parsimonious evolutionary histories by representing both substitutions
and double cut and join (DCJ) rearrangements in the presence of duplications.
The problem of constructing parsimonious history graphs thus subsumes related
maximum parsimony problems in the fields of phylogenetic reconstruction and
genome rearrangement. We show that tractable functions can be used to define
upper and lower bounds on the minimum number of substitutions and DCJ
rearrangements needed to explain any history graph. These bounds become tight
for a special type of unambiguous history graph called an ancestral variation
graph (AVG), which constrains in its combinatorial structure the number of
operations required. We finally demonstrate that for a given history graph ,
a finite set of AVGs describe all parsimonious interpretations of , and this
set can be explored with a few sampling moves.Comment: 52 pages, 24 figure
Node-weighted Steiner tree and group Steiner tree in planar graphs
We improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is Θ [theta] (logn), and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games.
The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log3 [superscript 3] n), or O(log2 [superscript 2] n) when the host graph is a tree. We obtain an O(log n polyloglog n) approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group
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