Exponents of Diophantine Approximation and Sturmian Continued Fractions

Let x be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents w_n(x) and w_n^*(x) defined by Mahler and Koksma. We calculate their six values when n=2 and x is a real number whose continued fraction expansion coincides with some Sturmian sequence of positive integers, up to the initial terms. In particular, we obtain the exact exponent of approximation to such a continued fraction x by quadratic surds.Comment: 25 page

ApproXFILTER - an approximative XML filter

Publish/subscribe systems filter published documents and inform their subscribers about documents matching their interests. Recent systems have focussed on documents or messages sent in XML format. Subscribers have to be familiar with the underlying XML format to create meaningful subscriptions. A service might support several providers with slightly differing formats, e.g., several publishers of books. This makes the definition of a successful subscription almost impossible. We propose the use of an approximative language for subscriptions.We introduce the design our ApproXFILTER algorithm for approximative filtering in a pub/sub system. We present the results of our analysis of a prototypical implementation

Measuring Internet performance within the organization.

Model; Evaluation; Performance; Secteur du tourisme; Systèmes d'information; Information technology; Internet;

N=4 BPS black holes and octonionic twistors

Stationary, spherically symmetric solutions of N=2 supergravity in 3+1 dimensions have been shown to correspond to holomorphic curves on the twistor space of the quaternionic-K\"ahler space which arises in the dimensional reduction along the time direction. In this note, we generalize this result to the case of 1/4-BPS black holes in N=4 supergravity, and show that they too can be lifted to holomorphic curves on a "twistor space" Z, obtained by fibering the Grassmannian F=SO(8)/U(4) over the moduli space in three-dimensions SO(8,n_v+2)/SO(8)xSO(n_v+2). This provides a kind of octonionic generalization of the standard constructions in quaternionic geometry, and may be useful for generalizing the known BPS black hole solutions, and finding new non-BPS extremal solutions.Comment: 30 pages, one figure, uses JHEP3.cl

Adaptive mesh refinements for thin shells whose middle surface is not exactly known

A strategy concerning mesh refinements for thin shells computation is presented. The geometry of the shell is given only by the reduced information consisting in nodes and normals on its middle surface corresponding to a coarse mesh. The new point is that the mesh refinements are defined from several criteria, including the transverse shear forces which do not appear in the mechanical energy of the applied shell formulation. Another important point is to be able to construct the unknown middle surface at each step of the refinement. For this, an interpolation method by edges, coupled with a triangle bisection algorithm, is applied. This strategy is illustrated on various geometries and mechanical problems

Approximative filtering of XML documents in a publish/subscribe system

Publish/subscribe systems filter published documents and inform their subscribers about documents matching their interests. Recent systems have focussed on documents or messages sent in XML format. Subscribers have to be familiar with the underlying XML format to create meaningful subscriptions. A service might support several providers with slightly differing formats, e.g., several publishers of books. This makes the definition of a successful subscription almost impossible. This paper proposes the use of an approximative language for subscriptions. We introduce the design of our ApproXFilter algorithm for approximative filtering in a publish/subscribe system. We present the results of our performance analysis of a prototypical implementation

Co-seismic deformation during the M_w 7.3 Aqaba earthquake (1995) from ERS-SAR interferometry

The M_w 7.3 1995 Aqaba earthquake is the largest instrumental earthquake along the Dead Sea Fault. We complement previous seismological studies by analyzing co‐seismic ground displacement from differential interferometry computed from ERS images spanning 3 different areas. They are compared with a synthetic model derived from seismological study. Only far‐field deformation related to the main sub‐event could be revealed because the near‐field area lies within the gulf. The interferometric data imply a 56 km long and 10 km wide fault segment, connecting the Elat Deep to the Aragonese Deep, which strikes N195°E and dips 65° to the west, with 2.1 m left‐lateral slip and a 15.5° rake indicating a slight normal component. The geodetic moment compares well with the seismic momen

Assessment of the notions of band offsets, wells and barriers at nanoscale semiconductor heterojunctions

Epitaxially-grown semiconductor heterostructures give the possibility to tailor the potential landscape for the carriers in a very controlled way. In planar lattice-matched heterostructures, the potential has indeed a very simple and easily predictable behavior: it is constant everywhere except at the interfaces where there is a step (discontinuity) which only depends on the composition of the semiconductors in contact. In this paper, we show that this universally accepted picture can be invalid in nanoscale heterostructures (e.g., quantum dots, rods, nanowires) which can be presently fabricated in a large variety of forms. Self-consistent tight-binding calculations applied to systems containing up to 75 000 atoms indeed demonstrate that the potential may have a more complex behavior in axial hetero-nanostructures: The band edges can show significant variations far from the interfaces if the nanostructures are not capped with a homogeneous shell. These results suggest new strategies to engineer the electronic properties of nanoscale objects, e.g. for sensors and photovoltaics.Comment: Accepted for publication in Phys. Rev.

Viscous fingering of miscible slices

Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a solute controlling the viscosity of miscible solutions. In contrast with fingering between two semi-infinite regions, fingering of finite slices is a transient phenomenon due to the decrease in time of the viscosity ratio across the interface induced by fingering and dispersion processes. We show that fingering contributes transiently to the broadening of the peak in time by increasing its variance. A quantitative analysis of the asymptotic contribution of fingering to this variance is conducted as a function of the four relevant parameters of the problem i.e. the log-mobility ratio R, the length of the slice l, the Peclet number Pe and the ratio between transverse and axial dispersion coefficients $\epsilon$. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.Comment: 10 pages, 13 figure