Monomial localizations and polymatroidal ideals

In this paper we consider monomial localizations of monomial ideals and conjecture that a monomial ideal is polymatroidal if and only if all its monomial localizations have a linear resolution. The conjecture is proved for squarefree monomial ideals where it is equivalent to a well-known characterization of matroids. We prove our conjecture in many other special cases. We also introduce the concept of componentwise polymatroidal ideals and extend several of the results known for polymatroidal ideals to this new class of ideals.     

Theoretical and experimental analysis of the electromechanical behavior of a compact spherical loudspeaker array for directivity control

Sound directivity control is made possible by a compact array of independent loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. The radiation pattern of spherical loudspeaker arrays has been predicted from the surface velocity pattern by approximating the drivers membranes as rigid vibrating spherical caps, although a rigorous assessment of this model has not been provided so far. Many aspects concerning compact array electromechanics remain unclear, such as the effects on the acoustical performance of the drivers interaction inside the array cavity, or the fact that voltages rather than velocities are controlled in practice. This work presents a detailed investigation of the electromechanical behavior of spherical loudspeaker arrays. Simulation results are shown to agree with laser vibrometer measurements and experimental sound power data obtained for a 12-driver spherical array prototype at low frequencies, whereas the non-rigid body motion and the first cavity eigenfrequency yield a discrepancy between theoretical and experimental results at high frequencies. Finally, although the internal acoustic coupling affects the drivers vibration in the low-frequency range, it does not play an important role on the radiated sound power.     

Wavelength conversion of nanosecond pulses to the mid-IR in photonic crystal fibers

We investigate degenerate four wave mixing with nanosecond pulses in fused silica photonic crystal fibers. Phase-matching curves are calculated taking into account the material and waveguide dispersion. Experiments with a nanosecond pulsed Nd:YAG pump laser and relatively short fiber lengths show more than an octave spanning conversion to idler and signal wavelengths at 3.105 μm and 0.642 μm, respectively. Conversion efficiency depends on the fiber length and pump intensity and is limited in our experiments by damage of the fiber input facet. Our results represent a new stretch towards the limit of the silica transmission window in the mid-infrared (IR).     

Sortable Freiman Ideals

In this paper, it is shown that a sortable ideal I is Freiman if and only if its sorted graph is chordal. This characterization is used to give a complete classification of Freiman principal Borel ideals and of Freiman Veronese-type ideals with constant bound.

     

Skeletons of monomial ideals

In analogy to the skeletons of a simplicial complex and their Stanley–Reisner ideals we introduce the skeletons of an arbitrary monomial ideal I ? S = K [x₁, …, x_n ]. This allows us to compute the depth of S /I in terms of its skeleton ideals. We apply these techniques to show that Stanley's conjecture on Stanley decompositions of S /I holds provided it holds whenever S /I is Cohen–Macaulay. We also discuss a conjecture of Soleyman Jahan and show that it suffices to prove his conjecture for monomial ideals with linear resolution (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of an elastic crane-trolley-load system - a case study for optimal control of coupled ODE-PDE systems

We present a mathematical model of a crane-trolley-load model, where the crane beam is subject to the partial differential equation (PDE) of static linear elasticity and the motion of the load is described by the dynamics of a pendulum that is fixed to a trolley moving along the crane beam. The resulting problem serves as a case study for optimal control of fully coupled partial and ordinary differential equations (ODEs). This particular type of coupled systems arises from many applications involving mechanical multi-body systems. We motivate the coupled ODE-PDE model, show its analytical well-posedness locally in time and examine the corresponding optimal control problem numerically by means of a projected gradient method with Broyden-Fletcher-Goldfarb-Shanno (BFGS) update.     

REDOR NMR: approaching structural elucidation of hydrated layers in silicate electrode glasses

Rotational echo double resonance (REDOR) is proposed as an alternative method for the structural determination of hydrated glasses, in particular of the incorporation of protons into the structure. First ²³N---¹H and ²⁷Al---¹H REDOR nuclear magnetic resonance data are presented for hydrated layers of electrode glasses of the system Na₂O---Al₂O₃---SiO₂ showing distinct differences of both the equilibrium amplitudes of the REDOR signals and the heteronuclear dipole couplings. The potential of this approach is demonstrated for kaolinite in terms of quantitative results.     

Quadrupole interaction studies of Hg in Sb

Time differential perturbed angular correlation and nuclear orientation studies of the electric quadrupole interaction for Hg in Sb have been performed. The effective field gradients |V _zz ^eff (HgSb)|=1.43(18)×10¹⁷V cm^–2 at room temperature andV _zz ^eff (HgSb)=+1.8(2) × 10¹⁷V cm^–2 below 0.05 K have been derived. These two values are no indication for an anomalous temperature dependence of the effective field gradient for Hg in Sb. The value of the electric field gradient fits well into the systematics for Hg in other hosts. It is shown that the electronic enhancements of the field gradients are correlated to the valence of the impurities and are rather insensitive to the host properties.On leave of absence from: University of Lisboa, Portugal     

A one-dimensional SiGe superlattice grown by UHV epitaxy

One-dimensional SiGe superlattices with periods ranging from 100 to 800 Å have been deposited on Si substrates by periodically varying the Ge content of a mixed Si_1-x Ge _x multilayer structure fromx=0 tox=0.15. The deposition was successful, employing and UHV evaporation technique at a substrate temperature of 750°C fulfilling the four conditions: Single crystal growth, no interdiffusion, two-dimensional growth, and pseudomorphic growth. It is shown that mismatch above 8 · 10^?3 favours growth by three-dimensional nucleation. The experimentally determined spacing of misfit dislocations is compared with theoretical results obtained by van der Merwe. The pseudomorphic growth behaviour of layers thinner than a critical thickness could be confirmed.     

Zum Schwingungsspektrum der Phosphorsäure. III. Dihydrogenphosphatlösungen,neubearbeitet mittels Laser-Ramanspektroskopie und mathematischer Resolvierung von Infrarotbanden

On the Vibrational Spectra of Phosphorus Acid. III. Dihydrogenphosphate Solutions Reinvestigated by means of Laser-Raman Spectroscopy and Mathematical Separation of the Infrared Bands Aqueous solutions of NaH₂PO₄ are reinvestigated by mathematical separation of the infrared bands between 700 and 1500 cm^?1 and by laser Raman spectroscopy. A single ion will not produce the spectra observed. It is possible to account for them assuming association of the anions into chains, which have a line group symmetry isomorphous with C_2h.