Fourier-Laplace transform of a variation of polarized complex Hodge structure, II

We show that the limit, by rescaling, of the `new supersymmetric index' attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of complex Hodge structure and prove a E_1 degeneration property for it.Comment: 51 pages, revised version, to appear in the proceedings volume of the conference `` New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry", RIMS, Kyoto, Jan. 7-11, 200

Stability Analysis of Closed Surge Tanks By Phase-Plane Method

The governing equations describing water level oscillations in a closed surge tank with compressed air at the top of the tank are a set of nonlinear ordinary differential equations if the hydraulic system is analyzed as a lumped system. These oscillations are stable or unstable depending on the parameters of the plant and the type and magnitude of the disturbance. The present available stability criterion has been developed by linearizing the governing equations and is, therefore, valid only for small disturbances. In the research reported herein, the governing equations are normalized to reduce the number of parameters from nine to four and the stability of oscillations is studied by using the phase plane method which allows inclusion of nonlinear terms in the analysis and, therefore, would be valid for small and large disturbances. Four cases of turbine flow demand are investigated. These are: constant discharge, constant gate opening, constant power and constant power combined with constant gate opening. Singularities of the governing equations are determined and analyzed in each case and stability criteria are developed. For illustration purposes, Driva Hydroelectric Power Plant System in Norway is analyzed and phase portraits are presented. These investigations show that the oscillations are always stable for the case of constant discharge and of constant gate opening. For the constant power case, oscillations are stable only if the system parameters satisfy certain criteria. For a combination of constant power and constant gate opening, it has been found that stability criteria for constant power are valid for heads greater than rated head and for constant gate opening for heads less than the rated head

The Abelian/Nonabelian Correspondence and Frobenius Manifolds

We propose an approach via Frobenius manifolds to the study (began in math.AG/0407254) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding ``abelianized'' quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.Comment: 35 pages, no figure

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

An extensible multilingual open source lemmatizer

We present GATE DictLemmatizer, a multilingual open source lemmatizer for the GATE NLP framework that currently supports English, German, Italian, French, Dutch, and Spanish, and is easily extensible to other languages. The software is freely available under the LGPL license. The lemmatization is based on the Helsinki Finite-State Transducer Technology (HFST) and lemma dictionaries automatically created from Wiktionary. We evaluate the performance of the lemmatizers against TreeTagger, which is only freely available for research purposes. Our evaluation shows that DictLemmatizer achieves similar or even better results than TreeTagger for languages where there is support from HFST. The performance drops when there is no support from HFST and the entire lemmatization process is based on lemma dictionaries. However, the results are still satisfactory given the fact that DictLemmatizer isopen-source and can be easily extended to other languages. The software for extending the lemmatizer by creating word lists from Wiktionary dictionaries is also freely available as open-source software

Femtosecond Pump-Probe Reflectivity Study of Silicon Carrier Dynamics

We have studied the ultrafast optical response of native-oxide terminated Si(001) with pump-probe reflectivity using 800 nm, 28 fs pulses at an excitation density of (5.5±0.3)×1018cm-3. Time-dependent reflectivity changes comprise third-order-response coherent-transient variations arising from anisotropic state filling and linear-response variations arising from excited free carriers, state filling, and lattice heating. A time constant of 32±5fs associated with momentum relaxation is extracted from the coherent-transient variations. The state-filling and free-carrier responses are sensitive to carrier temperature, allowing an electron-phonon energy relaxation time of 260±30fs to be measured. The recovery of the reflectivity signal back towards its initial value is largely governed surface recombination: a surface recombination velocity of (3±1)×104cm s-1 is deduced for native-oxide terminated Si(001)

A Compact Rotating-Mirror Autocorrelator Design for Femtosecond and Picosecond LaserPulses

An interferometric rapid-scanning autocorrelator employing two antiparallel rotating mirrors in a variable arm is optimized for maximum optical path difference as a function of the separation of the two rotating mirrors. A very compact design (mirror separation≈mirror diameter) is possible without a reduction in the maximum pulse width that can be measured

Measurement of Silicon Surface Recombination Velocity Using Ultrafast Pump-Probe Reflectivityin the Near Infrared

We demonstrate that ultrafast pump–probe reflectivity measurements from bulk Si samples using a Ti:sapphire femtosecond oscillator (λ=800 nm) can be used to measure the Si surface recombination velocity. The technique is sensitive to recombination velocities greater than ∼104 cm s−

Coherent Excitation of the Optic Phonon in Si: Transiently Stimulated Raman Scattering with aFinite-Lifetime Electronic Excitation

Using 28-fs, 800-nm laser pulses we have coherently excited and subsequently probed, with time-dependent reflectivity, the Si zone-center optic phonon. The phonon-induced reflectivity change ΔR∕R is well described by the response of an underdamped oscillator: ΔR∕R∝ exp(−t∕τph) cos(2πt∕Tph+ϕ). The measured phase ϕ indicates that transiently stimulated Raman scattering (TSRS) is responsible for the coherent-phonon generation: our results are in good agreement with a recent theory of TSRS for opaque materials [ T. E. Stevens et al. Phys. Rev. B 65 144304 (2002)] when we extend the theory to include the finite lifetime of the excited charge density that couples to the oscillation. We also discuss previous experimental results on Te, Bi, Sb, Si, and Ge in light of this extended theory. Additionally, our measured period Tph and decay time τph of the Si coherent oscillation are consistent with carrier-density-dependent Raman-scattering measurements