Hecke correspondences for smooth moduli spaces of sheaves

Publications mathématiques de l'IHÉS - We define functors on the derived category of the moduli space ℳ of stable sheaves on a smooth projective surface (under Assumptions A and...     

A derandomization using min-wise independent permutations

Min-wise independence is a recently introduced notion of limited independence, similar in spirit to pairwise independence. The latter has proven essential for the derandomization of many algorithms. Here we show that approximate min-wise independence allows similar uses, by presenting a derandomization of the RNC algorithm for approximate set cover due to S. Rajagopalan and V. Vazirani. We also discuss how to derandomize their set multi-cover and multi-set multi-cover algorithms in restricted cases. The multi-cover case leads us to discuss the concept of k-minima-wise independence, a natural counterpart to k-wise independence.     

Comparative Study of Sol-Gel and Coprecipitated Ni-Al Hydrotalcites

Hydrotalcite is an anionic clay mineral (layered double hydroxide) whose general formula is [M(II)_1–xM(III)_x(OH)₂]^x+X_x/n^n–·mH₂O. Anionic clays with a hydrotalcite-type are widely used as useful precursors of multicomponent catalysts. Hydrotalcites with Ni/Al molar ratio 2.5 have been synthesised both by the coprecipitation method, starting with nickel and aluminium nitrates and by the sol-gel method, using nickel acetylacetonate and aluminium isopropylate as precursors. The NiO-Al₂O₃ oxidic forms have been obtained by the thermal treatment of the precursors at 450°C and 900°C, respectively, and were characterised by DTA, XRD, IR spectroscopy and temperature programmed reduction (TPR). TPR clearly demonstrated a higher reducibility of the oxidic forms derived from the sol-gel synthesised precursors.     

Vertex Operators – From a Toy Model to Lattice Algebras

Within the framework of the discrete Wess–Zumino–Novikov–Witten theory we analyze the structure of vertex operators on a lattice. In particular, the lattice analogues of operator product expansions and braid relations are discussed. As the main physical application, a rigorous construction for the discrete counterpart g _n $ of the group valued field g(x) is provided. We study several automorphisms of the lattice algebras including discretizations of the evolution in the WZNW model. Our analysis is based on the theory of modular Hopf algebras and its formulation in terms of universal elements. Algebras of vertex operators and their structure constants are obtained for the deformed universal enveloping algebras . Throughout the whole paper, the abelian WZNW model is used as a simple example to illustrate the steps of our construction. Received: 16 December 1996 / Accepted: 5 May 1997     

Ground state of an exciton in a three-dimensional parabolic quantum dot: Convergent perturbative calculation

Working in the effective-mass approximation, we apply a powerful convergent perturbative technique of Turbiner's to the calculation of the ground state energy and the wave function of an exciton confined to a three-dimensional parabolic quantum dot. Unlike the usual Rayleigh–Schrödinger perturbation theory, Turbiner's approach works well even in the regime of strong coupling and does not require the knowledge of the full solution to the undisturbed problem. The second-order convergent calculation presented below is in excellent agreement with the results of exact numerical simulations for a wide range of system's confinement parameters.     

Nonlinear Integrated Optical Waveguides in Chalcogenide Glasses

This paper reports on the study and measurement of the third order optical nonlinearity in bulk sulfide-based chalcogenide glasses; The fabrication process of the ultrafast laser deposited As-S-(Se)-based chalcogenide films and optical waveguides using two techniques: wet chemistry etching and plasma etching.     

Transquantum Dynamics

Segal proposed transquantum commutation relations with two transquantum constants , besides Planck's quantum constant and with a variable i. The Heisenberg quantum algebra is a contraction—in a more general sense than that of Inönü and Wigner—of the Segal transquantum algebra. The usual constant i arises as a vacuum order-parameter in the quantum limit ,0. One physical consequence is a discrete spectrum for canonical variables and space-time coordinates. Another is an interconversion of time and energy accompanying space-time meltdown (disorder), with a fundamental conversion factor of some kilograms of energy per second.     

How Far can the Anisotropy Deviate from Uniaxiality in a Dy-Based Single-Molecule Magnet? Dinuclear Dy(III) Complex Study

The Dy^III ions in the dimer [Dy₂(H₂tea)₂(O₂CPh)₄]·2H₂O (1) (H₃tea = triethanolamine) have the 9-coordinate monocapped square-antiprismatic ligand field environment. Compound 1 shows slow relaxation of magnetization which is observable only with applied magnetic fields. This is consistent with the idea that low-symmetry ligand fields allow for the quantum tunneling of magnetization. This is reflected by the fact that there are no observable maxima in the out-of-phase ac susceptibility above 1.8 K. The {g}-tensor of the Dy^III ions {g _x = 11, g _y = 8.2, g _z = 1} further underlying the reduced uniaxiality in this system was determined in electron paramagnetic resonance (X- and Q-band) studies of 1 at temperatures down to 4 K.     

Ultrafast three-dimensional submicrometer-resolution readout of coherent optical-phonon oscillations with shaped unamplified laser pulses at 20 MHz

An ultrafast three-dimensional readout of coherent optical-phonon oscillations from a diamond film is demonstrated using temporally and spectrally shaped ultrashort laser pulses, delivered by a compact, oscillator-only laser system. This system integrates a long-cavity ytterbium-fiber-laser-pumped 30?fs Cr:forsterite oscillator with a photonic-crystal-fiber soliton frequency shifter and a periodically poled lithium niobate spectrum compressor, providing coherent Raman excitation and time-delayed interrogation of optical phonons in diamond at a 20?MHz repetition rate with a submicrometer spatial resolution.