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A dilation equation is a functional equation of the form f (t) = N k=0 c k f (2t − k), and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Hölder exponent of continuity of(More)
OBJECTIVE A chirp is a brief signal within which the frequency content changes rapidly. Spectrographic chirps are found in signals produced from many biological and physical phenomena. In radar and sonar engineering, signals with chirps are used to localize direction and range to the signal source. Although characteristic frequency changes during epileptic(More)
The refinement equation f (x) = N k=0 c k f (2x − k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. This paper explores the relationship of the refinement equation to the mapping τ (x) = 2x mod 1. A simple necessary condition for the existence of an integrable solution to the refinement equation is obtained by(More)
Measurements of charge-dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at sqrt[s(NN)] = 2.76 TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudorapidity range |η| < 0.8 are presented as a function of the collision centrality, particle separation in pseudorapidity, and(More)
Measurements of cross sections of inelastic and diffractive processes in proton–proton collisions at LHC energies were carried out with the ALICE detector. The fractions of diffractive processes in inelastic collisions were determined from a study of gaps in charged particle pseudora-pidity distributions: for single diffraction (diffractive mass
The yield of charged particles associated with high-p(t) trigger particles (8<p(t)<15 GeV/c) is measured with the ALICE detector in Pb-Pb collisions at √s(NN)=2.76 TeV relative to proton-proton collisions at the same energy. The conditional per-trigger yields are extracted from the narrow jetlike correlation peaks in azimuthal dihadron correlations. In the(More)
We report the measurements of correlations between event-by-event fluctuations of amplitudes of anisotropic flow harmonics in nucleus-nucleus collisions, obtained for the first time using a new analysis method based on multiparticle cumulants in mixed harmonics. This novel method is robust against systematic biases originating from nonflow effects and by(More)
In this Letter we report the first results on π(±), K(±), p, and p production at midrapidity (|y|<0.5) in central Pb-Pb collisions at sqrt[s(NN)] = 2.76 TeV, measured by the ALICE experiment at the LHC. The p(T) distributions and yields are compared to previous results at sqrt[s(NN)] = 200 GeV and expectations from hydrodynamic and thermal models. The(More)