222 research outputs found
Periods for flat algebraic connections
In previous work, we established a duality between the algebraic de Rham
cohomology of a flat algebraic connection on a smooth quasi-projective surface
over the complex numbers and the rapid decay homology of the dual connection
relying on a conjecture by C. Sabbah, which has been proved recently by T.
Mochizuki for algebraic connections in any dimension. In the present article,
we verify that Mochizuki's results allow to generalize these duality results to
arbitrary dimensions also
A construction of Frobenius manifolds with logarithmic poles and applications
A construction theorem for Frobenius manifolds with logarithmic poles is
established. This is a generalization of a theorem of Hertling and Manin. As an
application we prove a generalization of the reconstruction theorem of
Kontsevich and Manin for projective smooth varieties with convergent
Gromov-Witten potential. A second application is a construction of Frobenius
manifolds out of a variation of polarized Hodge structures which degenerates
along a normal crossing divisor when certain generation conditions are
fulfilled.Comment: 46 page
Analytic geometry of semisimple coalescent Frobenius structures
We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop "Asymptotic and Computational Aspects of Complex Differential Equations" at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians
Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients
We consider deformations of and matrix linear ODEs with
rational coefficients with respect to singular points of Fuchsian type which
don't satisfy the well-known system of Schlesinger equations (or its natural
generalization). Some general statements concerning reducibility of such
deformations for ODEs are proved. An explicit example of the general
non-Schlesinger deformation of -matrix ODE of the Fuchsian type with
4 singular points is constructed and application of such deformations to the
construction of special solutions of the corresponding Schlesinger systems is
discussed. Some examples of isomonodromy and non-isomonodromy deformations of
matrix ODEs are considered. The latter arise as the compatibility
conditions with linear ODEs with non-singlevalued coefficients.Comment: 15 pages, to appear in J. Phys.
Blowing up generalized Kahler 4-manifolds
We show that the blow-up of a generalized Kahler 4-manifold in a
nondegenerate complex point admits a generalized Kahler metric. As with the
blow-up of complex surfaces, this metric may be chosen to coincide with the
original outside a tubular neighbourhood of the exceptional divisor. To
accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.Comment: 16 page
Renormalized Perturbation Theory: A Missing Chapter
Renormalized perturbation theory \`a la BPHZ can be founded on causality as
analyzed by H. Epstein and V. Glaser in the seventies. Here, we list and
discuss a number of additional constraints of algebraic character some of which
have to be considered as parts of the core of the BPHZ framework.Comment: 16 page
The Hamiltonian Structure of the Second Painleve Hierarchy
In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable depending on n
parameters denoted by and . We introduce new
canonical coordinates and obtain Hamiltonians for the and
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates
Asperities and barriers on the seismogenic zone in North Chile: state-of-the-art after the 2007 Mw 7.7 Tocopilla earthquake inferred by GPS and InSAR data
The Mw 7.7 2007 November 14 earthquake had an epicentre located close to the city of Tocopilla, at the southern end of a known seismic gap in North Chile. Through modelling of Global Positioning System (GPS) and radar interferometry (InSAR) data, we show that this event ruptured the deeper part of the seismogenic interface (30–50 km) and did not reach the surface. The earthquake initiated at the hypocentre and was arrested ~150 km south, beneath the Mejillones Peninsula, an area already identified as an important structural barrier between two segments of the Peru–Chile subduction zone. Our preferred models for the Tocopilla main shock show slip concentrated in two main asperities, consistent with previous inversions of seismological data. Slip appears to have propagated towards relatively shallow depths at its southern extremity, under the Mejillones Peninsula. Our analysis of post-seismic deformation suggests that small but still significant post-seismic slip occurred within the first 10 d after the main shock, and that it was mostly concentrated at the southern end of the rupture. The post-seismic deformation occurring in this period represents ~12–19 per cent of the coseismic deformation, of which ~30–55 per cent has been released aseismically. Post-seismic slip appears to concentrate within regions that exhibit low coseismic slip, suggesting that the afterslip distribution during the first month of the post-seismic interval complements the coseismic slip. The 2007 Tocopilla earthquake released only ~2.5 per cent of the moment deficit accumulated on the interface during the past 130 yr and may be regarded as a possible precursor of a larger subduction earthquake rupturing partially or completely the 500-km-long North Chile seismic gap
Theory and Applications of X-ray Standing Waves in Real Crystals
Theoretical aspects of x-ray standing wave method for investigation of the
real structure of crystals are considered in this review paper. Starting from
the general approach of the secondary radiation yield from deformed crystals
this theory is applied to different concreat cases. Various models of deformed
crystals like: bicrystal model, multilayer model, crystals with extended
deformation field are considered in detailes. Peculiarities of x-ray standing
wave behavior in different scattering geometries (Bragg, Laue) are analysed in
detailes. New possibilities to solve the phase problem with x-ray standing wave
method are discussed in the review. General theoretical approaches are
illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table
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