121 research outputs found
Scale relativity and fractal space-time: theory and applications
In the first part of this contribution, we review the development of the
theory of scale relativity and its geometric framework constructed in terms of
a fractal and nondifferentiable continuous space-time. This theory leads (i) to
a generalization of possible physically relevant fractal laws, written as
partial differential equation acting in the space of scales, and (ii) to a new
geometric foundation of quantum mechanics and gauge field theories and their
possible generalisations. In the second part, we discuss some examples of
application of the theory to various sciences, in particular in cases when the
theoretical predictions have been validated by new or updated observational and
experimental data. This includes predictions in physics and cosmology (value of
the QCD coupling and of the cosmological constant), to astrophysics and
gravitational structure formation (distances of extrasolar planets to their
stars, of Kuiper belt objects, value of solar and solar-like star cycles), to
sciences of life (log-periodic law for species punctuated evolution, human
development and society evolution), to Earth sciences (log-periodic
deceleration of the rate of California earthquakes and of Sichuan earthquake
replicas, critical law for the arctic sea ice extent) and tentative
applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the
Evolution and Development of the Universe,8th - 9th October 2008, Paris,
Franc
Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
We extend the DuBois-Reymond necessary optimality condition and Noether's
symmetry theorem to the time delay variational setting. Both Lagrangian and
Hamiltonian versions of Noether's theorem are proved, covering problems of the
calculus of variations and optimal control with delays.Comment: This is a preprint of a paper whose final and definite form will
appear in the international journal Numerical Algebra, Control and
Optimization (NACO). Paper accepted for publication 15-March-201
Hahn's Symmetric Quantum Variational Calculus
We introduce and develop the Hahn symmetric quantum calculus with
applications to the calculus of variations. Namely, we obtain a necessary
optimality condition of Euler-Lagrange type and a sufficient optimality
condition for variational problems within the context of Hahn's symmetric
calculus. Moreover, we show the effectiveness of Leitmann's direct method when
applied to Hahn's symmetric variational calculus. Illustrative examples are
provided.Comment: This is a preprint of a paper whose final and definite form will
appear in the international journal Numerical Algebra, Control and
Optimization (NACO). Paper accepted for publication 06-Sept-201
The Hahn Quantum Variational Calculus
We introduce the Hahn quantum variational calculus. Necessary and sufficient
optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange
problems, are studied. We also show the validity of Leitmann's direct method
for the Hahn quantum variational calculus, and give explicit solutions to some
concrete problems. To illustrate the results, we provide several examples and
discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted:
18/June/2010; for publication in Journal of Optimization Theory and
Application
Arnold diffusion for a complete family of perturbations
In this work we illustrate the Arnold diffusion in a concrete example — the a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom H(p, q, I, f, s) = p2/2+ cos q - 1 + I2/2 + h(q, f, s; e) — proving that for any small periodic perturbation of the form h(q, f, s; e) = e cos q (a00 + a10 cosf + a01 cos s) (a10a01 ¿ 0) there is global instability for the action. For the proof we apply a geometrical mechanism based on the so-called scattering map. This work has the following structure: In the first stage, for a more restricted case (I* ~ p/2µ, µ = a10/a01), we use only one scattering map, with a special property: the existence of simple paths of diffusion called highways. Later, in the general case we combine a scattering map with the inner map (inner dynamics) to prove the more general result (the existence of instability for any µ). The bifurcations of the scattering map are also studied as a function of µ. Finally, we give an estimate for the time of diffusion, and we show that this time is primarily the time spent under the scattering map.Peer ReviewedPostprint (published version
Fractional variational calculus of variable order
We study the fundamental problem of the calculus of variations with variable
order fractional operators. Fractional integrals are considered in the sense of
Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the
authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted
13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The
Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck),
Operator Theory: Advances and Applications, Birkh\"auser Verlag
(http://www.springer.com/series/4850
Development of National Future Extreme Heat Scenario to Enable the Assessment of Climate Impacts on Public Health
The project's emphasis is on providing assessments of the magnitude, frequency and geographic distribution of EHEs to facilitate public health studies. We focus on the daily to weekly time scales on which EHEs occur, not on decadal-scale climate changes. There is, however, a very strong connection between air temperature patterns at the two time scales and long-term climatic changes will certainly alter the frequency of EHEs
Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the
epsilon-expansion of hypergeometric functions and their connection with Feynman
diagrams. In this paper, we show the following results:
Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth
(see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions.
Theorem B: The epsilon expansion of a hypergeometric function with one
half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the
harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are
ratios of polynomials. Some extra materials are available via the www at this
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected
and a few references added; v3: few references added
Health information seeking on the Internet: a double divide? Results from a representative survey in the Paris metropolitan area, France, 2005–2006
<p>Abstract</p> <p>Background</p> <p>The Internet is a major source of information for professionals and the general public, especially in the field of health. However, despite ever-increasing connection rates, a digital divide persists in the industrialised countries. The objective of this study was to assess the determinants involved in: 1) having or not having Internet access; and 2) using or not using the Internet to obtain health information.</p> <p>Methods</p> <p>A cross-sectional survey of a representative random sample was conducted in the Paris metropolitan area, France, in the fall of 2005 (n = 3023).</p> <p>Results</p> <p>Close to 70% of the adult population had Internet access, and 49% of Internet users had previously searched for medical information. Economic and social disparities observed in online health information seeking are reinforced by the economic and social disparities in Internet access, hence a double divide. While individuals who reported having a recent health problem were less likely to have Internet access (odds ratio (OR): 0.72, 95% confidence interval (CI): 0.53–0.98), it is they who, when they have Internet access, are the most likely to search for health information (OR = 1.44, 95% CI = 1.11–1.87).</p> <p>Conclusion</p> <p>In the French context of universal health insurance, access to the Internet varies according to social and socioeconomic status and health status, and its use for health information seeking varies also with health beliefs, but not to health insurance coverage or health-care utilisation. Certain economic and social inequalities seem to impact cumulatively on Internet access and on the use of the Internet for health information seeking. It is not obvious that the Internet is a special information tool for primary prevention in people who are the furthest removed from health concerns. However, the Internet appears to be a useful complement for secondary prevention, especially for better understanding health problems or enhancing therapeutic compliance.</p
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation
We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any δ[much less-than]1,K [much greater-than] 1, s > 1, we construct smooth initial data u 0 with ||u0||Hs , so that the corresponding time evolution u satisfies u(T)Hs[greater than]K at some time T. This growth occurs despite the Hamiltonian’s bound on ||u(t)||H1 and despite the conservation of the quantity ||u(t)||L2.
The proof contains two arguments which may be of interest beyond the particular result described above. The first is a construction of the solution’s frequency support that simplifies the system of ODE’s describing each Fourier mode’s evolution. The second is a construction of solutions to these simpler systems of ODE’s which begin near one invariant manifold and ricochet from arbitrarily small neighborhoods of an arbitrarily large number of other invariant manifolds. The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems
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