287 research outputs found
Fractional Euler-Lagrange differential equations via Caputo derivatives
We review some recent results of the fractional variational calculus.
Necessary optimality conditions of Euler-Lagrange type for functionals with a
Lagrangian containing left and right Caputo derivatives are given. Several
problems are considered: with fixed or free boundary conditions, and in
presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will
appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu
et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in
pres
On finite -groups whose automorphisms are all central
An automorphism of a group is said to be central if
commutes with every inner automorphism of . We construct a family of
non-special finite -groups having abelian automorphism groups. These groups
provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math.,
{\bf 165} (2008), 161 - 187]. We also construct a family of finite -groups
having non-abelian automorphism groups and all automorphisms central. This
solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice,
Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math.,
{\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in
201
Investigation of the thermal stability of Mg/Co periodic multilayers for EUV applications
We present the results of the characterization of Mg/Co periodic multilayers
and their thermal stability for the EUV range. The annealing study is performed
up to a temperature of 400\degree C. Images obtained by scanning transmission
electron microscopy and electron energy loss spectroscopy clearly show the good
quality of the multilayer structure. The measurements of the EUV reflectivity
around 25 nm (~49 eV) indicate that the reflectivity decreases when the
annealing temperature increases above 300\degreeC. X-ray emission spectroscopy
is performed to determine the chemical state of the Mg atoms within the Mg/Co
multilayer. Nuclear magnetic resonance used to determine the chemical state of
the Co atoms and scanning electron microscopy images of cross sections of the
Mg/Co multilayers reveal changes in the morphology of the stack from an
annealing temperature of 305\degreee;C. This explains the observed reflectivity
loss.Comment: Published in Applied Physics A: Materials Science \& Processing
Published at
http://www.springerlink.com.chimie.gate.inist.fr/content/6v396j6m56771r61/ 21
page
Time-Fractional Optimal Control of Initial Value Problems on Time Scales
We investigate Optimal Control Problems (OCP) for fractional systems
involving fractional-time derivatives on time scales. The fractional-time
derivatives and integrals are considered, on time scales, in the
Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient
conditions for existence and uniqueness of solution to initial value problems
described by fractional order differential equations on time scales are known.
Here we consider a fractional OCP with a performance index given as a
delta-integral function of both state and control variables, with time evolving
on an arbitrarily given time scale. Interpreting the Euler--Lagrange first
order optimality condition with an adjoint problem, defined by means of right
Riemann--Liouville fractional delta derivatives, we obtain an optimality system
for the considered fractional OCP. For that, we first prove new fractional
integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book
chapter with Springer International Publishing AG. Submitted 23/Jan/2019;
revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial
text overlap with arXiv:1508.0075
Musical Ratios in Sounds from the Human Cochlea
The physiological roots of music perception are a matter of long-lasting debate. Recently light on this problem has been shed by the study of otoacoustic emissions (OAEs), which are weak sounds generated by the inner ear following acoustic stimulation and, sometimes, even spontaneously. In the present study, a high-resolution time–frequency method called matching pursuit was applied to the OAEs recorded from the ears of 45 normal volunteers so that the component frequencies, amplitudes, latencies, and time-spans could be accurately determined. The method allowed us to find that, for each ear, the OAEs consisted of characteristic frequency patterns that we call resonant modes. Here we demonstrate that, on average, the frequency ratios of the resonant modes from all the cochleas studied possessed small integer ratios. The ratios are the same as those found by Pythagoras as being most musically pleasant and which form the basis of the Just tuning system. The statistical significance of the results was verified against a random distribution of ratios. As an explanatory model, there are attractive features in a recent theory that represents the cochlea as a surface acoustic wave resonator; in this situation the spacing between the rows of hearing receptors can create resonant cavities of defined lengths. By adjusting the geometry and the lengths of the resonant cavities, it is possible to generate the preferred frequency ratios we have found here. We conclude that musical perception might be related to specific geometrical and physiological properties of the cochlea
Measurement and comparison of individual external doses of high-school students living in Japan, France, Poland and Belarus -- the "D-shuttle" project --
Twelve high schools in Japan (of which six are in Fukushima Prefecture), four
in France, eight in Poland and two in Belarus cooperated in the measurement and
comparison of individual external doses in 2014. In total 216 high-school
students and teachers participated in the study. Each participant wore an
electronic personal dosimeter "D-shuttle" for two weeks, and kept a journal of
his/her whereabouts and activities. The distributions of annual external doses
estimated for each region overlap with each other, demonstrating that the
personal external individual doses in locations where residence is currently
allowed in Fukushima Prefecture and in Belarus are well within the range of
estimated annual doses due to the background radiation level of other
regions/countries
Hepatitis C virus quasispecies in chronically infected children subjected to interferon–ribavirin therapy
Accumulating evidence suggests that certain features of hepatitis C virus (HCV), especially its high genetic variability, might be responsible for the low efficiency of anti-HCV treatment. Here, we present a bioinformatic analysis of HCV-1a populations isolated from 23 children with chronic hepatitis C (CHC) subjected to interferon–ribavirin therapy. The structures of the viral quasispecies were established based on a 132-amino-acid sequence derived from E1/E2 protein, including hypervariable region 1 (HVR1). Two types of HCV populations were identified. The first type, found in non-responders, contained a small number of closely related variants. The second type, characteristic for sustained responders, was composed of a large number of distantly associated equal-rank variants. Comparison of 445 HVR1 sequences showed that a significant number of variants present in non-responding patients are closely related, suggesting that certain, still unidentified properties of the pathogen may be key factors determining the result of CHC treatment
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