3,970 research outputs found
The structure of decomposition of a triconnected graph
We describe the structure of triconnected graph with the help of its
decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph
into rather small groups with a simple structure, named complexes. The detailed
description of all complexes is presented. Moreover, we prove that the
structure of a hypertree could be introduced on the set of all complexes. This
structure gives us a complete description of the relative disposition of the
complexes.
Keywords: connectivity, triconneted graphs.Comment: 49 pages, 8 figures. Russian version published in Zap. Nauchn. Sem.
POMI v.391 (2011), http://www.pdmi.ras.ru/znsl/2011/v391/abs090.htm
Superheavies: Theoretical incitements and predictions
It is well known that in fusion reactions one may get only neutron deficient
superheavy nuclei located far from the island of stability. The multi-nucleon
transfer reactions allow one to produce more neutron enriched new heavy nuclei
but the corresponding cross sections are rather low. Neutron capture process is
considered here as alternative method for production of long-lived neutron rich
superheavy nuclei. Strong neutron fluxes might be provided by nuclear reactors
and nuclear explosions in laboratory frame and by supernova explosions in
nature. All these cases are discussed in the paper.Comment: 7 FIGURE
Curvature Correction in the Strutinsky's Method
Mass calculations carried out by Strutinsky's shell correction method are
based on the notion of smooth single particle level density. The smoothing
procedure is always performed using curvature correction. In the presence of
curvature correction a smooth function remains unchanged if smoothing is
applied. Two new curvature correction methods are introduced. The performance
of the standard and new methods are investigated using harmonic oscillator and
realistic potentials.Comment: 4 figures, submitted to Journal of Physics G: Nuclear and Particle
Physic
Spectroscopic studies of fractal aggregates of silver nanospheres undergoing local restructuring
We present an experimental spectroscopic study of large random colloidal
aggregates of silver nanoparticles undergoing local restructuring. We argue
that such well-known phenomena as strong fluctuation of local electromagnetic
fields, appearance of "hot spots" and enhancement of nonlinear optical
responses depend on the local structure on the scales of several nanosphere
diameters, rather that the large-scale fractal geometry of the sample.Comment: 3.5 pages, submitted to J. Chem. Phy
What is moving in silica at 1 K? A computer study of the low-temperature anomalies
Though the existence of two-level systems (TLS) is widely accepted to explain
low temperature anomalies in many physical observables, knowledge about their
properties is very rare. For silica which is one of the prototype glass-forming
systems we elucidate the properties of the TLS via computer simulations by
applying a systematic search algorithm. We get specific information in the
configuration space, i.e. about relevant energy scales, the absolute number of
TLS and electric dipole moments. Furthermore important insight about the
real-space realization of the TLS can be obtained. Comparison with experimental
observations is included
Parameterized Complexity of Secluded Connectivity Problems
The Secluded Path problem models a situation where a sensitive information
has to be transmitted between a pair of nodes along a path in a network. The
measure of the quality of a selected path is its exposure, which is the total
weight of vertices in its closed neighborhood. In order to minimize the risk of
intercepting the information, we are interested in selecting a secluded path,
i.e. a path with a small exposure. Similarly, the Secluded Steiner Tree problem
is to find a tree in a graph connecting a given set of terminals such that the
exposure of the tree is minimized. The problems were introduced by Chechik et
al. in [ESA 2013]. Among other results, Chechik et al. have shown that Secluded
Path is fixed-parameter tractable (FPT) on unweighted graphs being
parameterized by the maximum vertex degree of the graph and that Secluded
Steiner Tree is FPT parameterized by the treewidth of the graph. In this work,
we obtain the following results about parameterized complexity of secluded
connectivity problems.
We give FPT-algorithms deciding if a graph G with a given cost function
contains a secluded path and a secluded Steiner tree of exposure at most k with
the cost at most C.
We initiate the study of "above guarantee" parameterizations for secluded
problems, where the lower bound is given by the size of a Steiner tree.
We investigate Secluded Steiner Tree from kernelization perspective and
provide several lower and upper bounds when parameters are the treewidth, the
size of a vertex cover, maximum vertex degree and the solution size. Finally,
we refine the algorithmic result of Chechik et al. by improving the exponential
dependence from the treewidth of the input graph.Comment: Minor corrections are don
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