78,570 research outputs found
Nature of Decoupling in the Mixed Phase of Extremely Type-II Layered Superconductors
The uniformly frustrated layered XY model is analyzed in its Villain form. A
decouple pancake vortex liquid phase is identified. It is bounded by both
first-order and second-order decoupling lines in the magnetic field versus
temperature plane. These transitions, respectively, can account for the
flux-lattice melting and for the flux-lattice depinning observed in the mixed
phase of clean high-temperature superconductors.Comment: 11 pages of PLAIN TeX, 1 postscript figure, published version, many
change
On defensive alliances and line graphs
Let be a simple graph of size and degree sequence . Let denotes the line graph of
. The aim of this paper is to study mathematical properties of the
alliance number, , and the global alliance number,
, of the line graph of a simple graph. We show
that In particular, if is a -regular
graph (), then , and if is a
-semiregular bipartite graph, then . As a consequence of
the study we compare and , and we
characterize the graphs having . Moreover, we show that
the global-connected alliance number of is bounded by
where
denotes the diameter of , and we show that the global
alliance number of is bounded by . The case of
strong alliances is studied by analogy
Topological defects and misfit strain in magnetic stripe domains of lateral multilayers with perpendicular magnetic anisotropy
Stripe domains are studied in perpendicular magnetic anisotropy films
nanostructured with a periodic thickness modulation that induces the lateral
modulation of both stripe periods and inplane magnetization. The resulting
system is the 2D equivalent of a strained superlattice with properties
controlled by interfacial misfit strain within the magnetic stripe structure
and shape anisotropy. This allows us to observe, experimentally for the first
time, the continuous structural transformation of a grain boundary in this 2D
magnetic crystal in the whole angular range. The magnetization reversal process
can be tailored through the effect of misfit strain due to the coupling between
disclinations in the magnetic stripe pattern and domain walls in the in-plane
magnetization configuration
Offensive alliances in cubic graphs
An offensive alliance in a graph is a set of vertices
where for every vertex in its boundary it holds that the
majority of vertices in 's closed neighborhood are in . In the case of
strong offensive alliance, strict majority is required. An alliance is
called global if it affects every vertex in , that is, is a
dominating set of . The global offensive alliance number
(respectively, global strong offensive alliance number
) is the minimum cardinality of a global offensive
(respectively, global strong offensive) alliance in . If has
global independent offensive alliances, then the \emph{global independent
offensive alliance number} is the minimum cardinality among
all independent global offensive alliances of . In this paper we study
mathematical properties of the global (strong) alliance number of cubic graphs.
For instance, we show that for all connected cubic graph of order ,
where
denotes the line graph of . All the above bounds are tight
Global defensive k-alliances in graphs
Let be a simple graph. For a nonempty set , and
a vertex , denotes the number of neighbors has in
. A nonempty set is a \emph{defensive -alliance} in
if A
defensive -alliance is called \emph{global} if it forms a dominating
set. The \emph{global defensive -alliance number} of , denoted by
, is the minimum cardinality of a defensive
-alliance in . We study the mathematical properties of
The Gremlin Graph Traversal Machine and Language
Gremlin is a graph traversal machine and language designed, developed, and
distributed by the Apache TinkerPop project. Gremlin, as a graph traversal
machine, is composed of three interacting components: a graph , a traversal
, and a set of traversers . The traversers move about the graph
according to the instructions specified in the traversal, where the result of
the computation is the ultimate locations of all halted traversers. A Gremlin
machine can be executed over any supporting graph computing system such as an
OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph
traversal language, is a functional language implemented in the user's native
programming language and is used to define the of a Gremlin machine.
This article provides a mathematical description of Gremlin and details its
automaton and functional properties. These properties enable Gremlin to
naturally support imperative and declarative querying, host language
agnosticism, user-defined domain specific languages, an extensible
compiler/optimizer, single- and multi-machine execution models, hybrid depth-
and breadth-first evaluation, as well as the existence of a Universal Gremlin
Machine and its respective entailments.Comment: To appear in the Proceedings of the 2015 ACM Database Programming
Languages Conferenc
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