4,684 research outputs found
Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
We introduce the framework of path-complete graph Lyapunov functions for
approximation of the joint spectral radius. The approach is based on the
analysis of the underlying switched system via inequalities imposed among
multiple Lyapunov functions associated to a labeled directed graph. Inspired by
concepts in automata theory and symbolic dynamics, we define a class of graphs
called path-complete graphs, and show that any such graph gives rise to a
method for proving stability of the switched system. This enables us to derive
several asymptotically tight hierarchies of semidefinite programming
relaxations that unify and generalize many existing techniques such as common
quadratic, common sum of squares, and maximum/minimum-of-quadratics Lyapunov
functions. We compare the quality of approximation obtained by certain classes
of path-complete graphs including a family of dual graphs and all path-complete
graphs with two nodes on an alphabet of two matrices. We provide approximation
guarantees for several families of path-complete graphs, such as the De Bruijn
graphs, establishing as a byproduct a constructive converse Lyapunov theorem
for maximum/minimum-of-quadratics Lyapunov functions.Comment: To appear in SIAM Journal on Control and Optimization. Version 2 has
gone through two major rounds of revision. In particular, a section on the
performance of our algorithm on application-motivated problems has been added
and a more comprehensive literature review is presente
Infrared spectra of C2H4 dimer and trimer
Spectra of ethylene dimers and trimers are studied in the nu11 and (for the
dimer) nu9 fundamental band regions of C2H4 (~2990 and 3100 cm-1) using a
tunable optical parametric oscillator source to probe a pulsed supersonic slit
jet expansion. The deuterated trimer has been observed previously, but this
represents the first rotationally resolved spectrum of (C2H4)3. The results
support the previously determined cross-shaped (D2d) dimer and barrel-shaped
(C3h or C3) trimer structures. However, the dimer spectrum in the nu9
fundamental region of C2H4 is apparently very perturbed and a previous
rotational analysis is not well verified.Comment: 21 pages, 4 figure
Biodiversity of benthic invertebrates in Aras River
Benthic invertebrate species and their change was studied in Aras River during a hydro- biological research on the middle and terminal parts of Aras River that spanned the years 1995-1996 and 2005-2006. We found 91 species of benthic invertebrates of which 85 species were identified during 1995-1996 and 49 species during 2005-2006. The highest rate of biodiversity was seen in molluscs with 19 species and chironomid larvae with 17 species. Forty-two species had wide distribution and the remaining occurred only in special habitats. The biomass of invertebrates reduced from the upper reach of the river to the middle and lower reaches because of the changes in river bed from soil to sand. It is concluded that the formation of different habitats in different sections of the Aras River has a crucial role in the change observed in biodiversity of the benthic invertebrates
An asymptotic unsteady lifting-line theory with energetics and optimum motion of thrust-producing lifting surfaces
A low frequency unsteady lifting-line theory is developed for a harmonically oscillating wing of large aspect ratio. The wing is assumed to be chordwise rigid but completely flexible in the span direction. The theory is developed by use of the method of matched asymptotic expansions which reduces the problem from a singular integral equation to quadrature. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. The influence of reduced frequency, aspect ratio, planform shape, and mode of oscillation on wing aerodynamics is demonstrated through numerical examples. Compared with lifting-surface theory, computation time is reduced significantly. Using the present theory, the energetic quantities associated with the propulsive performance of a finite wing oscillating in combined pitch and heave are obtained in closed form. Numerical examples are presented for an elliptic wing
An experimental investigation of the chopping of helicopter main rotor tip vortices by the tail rotor
The chopping of helicopter main rotor tip vortices by the tail rotor was experimentally investigated. This is a problem of blade vortex interaction (BVI) at normal incidence where the vortex is generally parallel to the rotor axis. The experiment used a model rotor and an isolated vortex and was designed to isolate BVI noise from other types of rotor noise. Tip Mach number, radical BVI station, and free stream velocity were varied. Fluctuating blade pressures, farfield sound pressure level and directivity, velocity field of the incident vortex, and blade vortex interaction angles were measured. Blade vortex interaction was found to produce impulsive noise which radiates primarily ahead of the blade. For interaction away from the blade tip, the results demonstrate the dipole character of BVI radiation. For BVI close to the tip, three dimensional relief effect reduces the intensity of the interaction, despite larger BVI angle and higher local Mach number. Furthermore, in this case, the radiation patern is more complex due to diffraction at and pressure communication around the tip
Three new infrared bands of the He-OCS complex
Three new infrared bands of the weakly-bound He-OCS complex are studied,
using tunable lasers to probe a pulsed supersonic slit jet expansion. They
correspond to the (0400) <-- (0000), (1001)<-- (0000), and (0401) <-- (0000)
transitions of OCS at 2105, 2918, and 2937 cm-1, respectively. The latter band
is about 7900 times weaker than the previously studied OCS nu1 fundamental.
Vibrational shifts relative to the free OCS monomer are found to be additive.
Since carbonyl sulfide has previously been shown to be a valuable probe of
superfluid quantum solvation effects in helium clusters and droplets, the
present results could be useful for future studies of vibrational effects in
such systems.Comment: 16 pages, 1 figure, 4 table
Oro-Dental Health Status and Salivary Characteristics in Children with Chronic Renal Failure
Children suffering from decreased renal function may demand unique considerations regarding special oral and dental conditions they are encountered to. It is mentioned that renal function deterioration may affect the hard or soft tissues of the mouth. Having knowledge about the high prevalence of dental defects, calculus, gingival hyperplasia, modified salivary composition and tissue responses to the dental plaque may aid the physician and the dentist to help nurture the patient with chronic renal failure through the crisis, with an aesthetically satisfying and functioning dentition
Dimension Reduction via Colour Refinement
Colour refinement is a basic algorithmic routine for graph isomorphism
testing, appearing as a subroutine in almost all practical isomorphism solvers.
It partitions the vertices of a graph into "colour classes" in such a way that
all vertices in the same colour class have the same number of neighbours in
every colour class. Tinhofer (Disc. App. Math., 1991), Ramana, Scheinerman, and
Ullman (Disc. Math., 1994) and Godsil (Lin. Alg. and its App., 1997)
established a tight correspondence between colour refinement and fractional
isomorphisms of graphs, which are solutions to the LP relaxation of a natural
ILP formulation of graph isomorphism.
We introduce a version of colour refinement for matrices and extend existing
quasilinear algorithms for computing the colour classes. Then we generalise the
correspondence between colour refinement and fractional automorphisms and
develop a theory of fractional automorphisms and isomorphisms of matrices.
We apply our results to reduce the dimensions of systems of linear equations
and linear programs. Specifically, we show that any given LP L can efficiently
be transformed into a (potentially) smaller LP L' whose number of variables and
constraints is the number of colour classes of the colour refinement algorithm,
applied to a matrix associated with the LP. The transformation is such that we
can easily (by a linear mapping) map both feasible and optimal solutions back
and forth between the two LPs. We demonstrate empirically that colour
refinement can indeed greatly reduce the cost of solving linear programs
A Complete Characterization of the Gap between Convexity and SOS-Convexity
Our first contribution in this paper is to prove that three natural sum of
squares (sos) based sufficient conditions for convexity of polynomials, via the
definition of convexity, its first order characterization, and its second order
characterization, are equivalent. These three equivalent algebraic conditions,
henceforth referred to as sos-convexity, can be checked by semidefinite
programming whereas deciding convexity is NP-hard. If we denote the set of
convex and sos-convex polynomials in variables of degree with
and respectively, then our main
contribution is to prove that if and
only if or or . We also present a complete
characterization for forms (homogeneous polynomials) except for the case
which is joint work with G. Blekherman and is to be published
elsewhere. Our result states that the set of convex forms in
variables of degree equals the set of sos-convex forms if
and only if or or . To prove these results, we present
in particular explicit examples of polynomials in
and
and forms in
and , and a
general procedure for constructing forms in from nonnegative but not sos forms in variables and degree .
Although for disparate reasons, the remarkable outcome is that convex
polynomials (resp. forms) are sos-convex exactly in cases where nonnegative
polynomials (resp. forms) are sums of squares, as characterized by Hilbert.Comment: 25 pages; minor editorial revisions made; formal certificates for
computer assisted proofs of the paper added to arXi
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