Generalized Euler-Lagrange equations for variational problems with scale derivatives

We obtain several Euler-Lagrange equations for variational functionals defined on a set of H\"older curves. The cases when the Lagrangian contains multiple scale derivatives, depends on a parameter, or contains higher-order scale derivatives are considered.Comment: Submitted on 03-Aug-2009; accepted for publication 16-March-2010; in "Letters in Mathematical Physics"

A λ-lemma for Normally Hyperbolic Invariant Manifolds

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A potential use for the C-band polarimetric SAR parameters to characterise the soil surface over bare agriculture fields

The objective of this study was to analyze the potential of the C-band polarimetric SAR parameters for the soil surface characterization of bare agricultural soils. RADARSAT-2 data and simulations using the Integral Equation Model (IEM) were analyzed to evaluate the polarimetric SAR parameters' sensitivities to the soil moisture and surface roughness. The results showed that the polarimetric parameters in the C-band were not very relevant to the characterization of the soil surface over bare agricultural areas. Low dynamics were often observed between the polarimetric parameters and both the soil moisture content and the soil surface roughness. These low dynamics do not allow for the accurate estimation of the soil parameters, but they could augment the standard inversion approaches to improve the estimation of these soil parameters. The polarimetric parameter alpha_1 could be used to detect very moist soils (>30%), while the anisotropy could be used to separate the smooth soils

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

Canonical Melnikov theory for diffeomorphisms

We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or Melnikov displacement can be written in a canonical way. This function is defined to be a section of the normal bundle of the saddle connection. We show how our definition reproduces the classical methods of Poincar\'{e} and Melnikov and specializes to methods previously used for exact symplectic and volume-preserving maps. We use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the Melnikov displacement.Comment: laTeX, 31 pages, 3 figure

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

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

In vitro inhibition of human sarcoma cells' invasive ability by bis(5-amidino-2-benzimidazolyl)methane--a novel esteroprotease inhibitor.

Bis(5-amidino-2-benzimidazolyl)methane (BABIM) is a synthetic aromatic amidine compound which has a number of important biochemical effects, including inhibition of a family of esteroproteases (trypsin, urokinase, plasmin) previously linked to the complex process of tumor invasion. Previous work has suggested that exogenous natural protease inhibitors can block invasion of tumor cells across basement membranes (BM) in vitro. The authors studied the effect of BABIM on the human cell line HT-1080 with the use of a quantitative in vitro amnion invasion assay system. They have verified the ability of these cells to grow in nude mice and metastasize via the lymphatics or blood vessels on the basis of the route of administration of the inoculum. Cells which were able to actively cross the entire BM were trapped on filters and counted by both brightfield microscopy and by beta scintillation counting of cells whose DNA was labeled with tritiated thymidine. In agreement with either counting technique, BABIM, at a concentration of 10(-4) M, significantly inhibited invasion (P less than 0.005) over the 7-day course of the experiments. Under these conditions, the inhibitor was nontoxic and did not alter the attachment of the cells to the amniotic membrane. Furthermore, a highly significant inhibition of invasion (P less than 0.001) was also demonstrated across a variation in molar concentration of BABIM of more than 2 orders of magnitude. Most remarkably, cells were initially inhibited in their ability to invade in the presence of between 10(-9) and 10(-3) M BABIM. Measurement of Type IV specific collagenase in media from these cells shows a significant inhibition of activity in the presence of BABIM. These results suggest two, not necessarily exclusive, alternative interpretations: first, that inhibition of the proteolytic steps along the pathway of activation of basement membrane degrading enzymes results in inhibition of invasion; second, that arginine directed esteroproteases may work in concert with cellular collagenolytic metalloproteinases in the process of invasion by human tumor cells through native matrix barriers

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

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