A family of cohen-macaulay modules over singularities of type xt + y3

Let K be a field with char K ≠ 3 and it two positive integers such that 1 ≤i <t/2,t ≠ 3i. The classification problem for maximal Cohen-Macaulay modules over K[[X,Y]]/(X^t+Y³ ) is complicated if t≥ 6, because there exist parameter families of non-isomorphic maximal Cohen-Macaulay modules [Sc], or [GK], [Yo, Ch.9] and [DG]). Here we describe parameter families of such modules N, such that N/YN is a direct sum of copies of K[[X]]/(X ⁱ)K[[X]]/(X^t-i ).     

Multilayered catalysts for fatty acid ester hydrotreatment into fuel range hydrocarbons

This study aims to investigate Ni–Mo/γAl₂O₃ and Ni–La/Zn-ZSM-5–γAl₂O₃ catalysts, which convert methyl esters into various compounds with a similar composition to those found in diesel fuels. The catalysts were synthesized by impregnation using two different routes and characterized by atomic absorption spectrometry, Brunauer–Emmett–Teller, and scanning electron microscopy. The acid strength distribution indicates a relatively high concentration of weak acid centers for both materials. The disposal of the catalysts into the reactor system is an important factor for driving the process toward the desired reaction products. The hydrodeoxygenation becomes important and paraffins are formed as intermediaries when Ni–Mo/γAl₂O₃ is first disposed into the reactor, whereas hydrocracking is poor and the dehydrocyclization does not occur in the case of Ni–La/Zn-ZSM-5–γAl₂O₃ as first layer. Triple-layered catalytic systems enhance the production of n-paraffins with high carbon number, mainly C17 and C18, which are important as diesel component. The effect of temperature was also studied and it was found that aromatics are mainly formed over double-layered catalytic systems by varying the temperature. In the case of triple-layered catalysts, the change in the product composition from saturated hydrocarbons with 12–18 carbon atoms to aromatics was observed by increasing the temperature from 420 to 445 °C. An interesting finding by the addition of n-octane in the feed was observed and the considerable increase in C8 aromatics involved the dehydrocyclization that occurred faster than hydrocracking.     

Simple General Neron Desingularization in local Q-algebras

We give here an easier proof of the so-called General Neron Desingularization in the frame of local algebras.     

Orthogonal exponentials, translations, and Bohr completions

We are concerned with an harmonic analysis in Hilbert spaces L²(μ), where μ is a probability measure on . The unifying question is the presence of families of orthogonal (complex) exponentials e_λ(x)=exp(2πiλx) in L²(μ). This question in turn is connected to the existence of a natural embedding of L²(μ) into an L²-space of Bohr almost periodic functions on . In particular we explore when L²(μ) contains an orthogonal basis of e_λ functions, for λ in a suitable discrete subset in ; i.e, when the measure μ is spectral. We give a new characterization of finite spectral sets in terms of the existence of a group of local translation. We also consider measures μ that arise as fixed points (in the sense of Hutchinson) of iterated function systems (IFSs), and we specialize to the case when the function system in the IFS consists of affine and contractive mappings in . We show in this case that if μ is then assumed spectral then its partitions induced by the IFS at hand have zero overlap measured in μ. This solves part of the Łaba–Wang conjecture. As an application of the new non-overlap result, we solve the spectral-pair problem for Bernoulli convolutions advancing in this way a theorem of Ka-Sing Lau. In addition we present a new perspective on spectral measures and orthogonal Fourier exponentials via the Bohr compactification.     

A duality principle for groups

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L²(Rd) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups. We examine the existence problem of dual pairs and establish some connection with classification problems for II₁ factors. While in general such a pair may not exist for some groups, we show that such a dual pair always exists for every subrepresentation of the left regular unitary representation when G is an abelian infinite countable group or an amenable ICC group. For free groups with finitely many generators, the existence problem of such a dual pair is equivalent to the well-known problem about the classification of free group von Neumann algebras.     

The quantitative Faber–Krahn inequality for the Robin Laplacian

We prove a quantitative form of the Faber–Krahn inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions. The asymmetry term involves the square power of the Fraenkel asymmetry, multiplied by a constant depending on the Robin parameter, the dimension of the space and the measure of the set.     

The incompressible limit of the full Navier–Stokes–Fourier system on domains with rough boundaries

We study the incompressible limit of the full Navier–Stokes–Fourier system on condition that the boundary of the spatial domain oscillates with the amplitude and wave length proportional to the Mach number. Assuming the fluid satisfies the complete slip boundary conditions on the oscillating boundary, we identify the asymptotic limit, and, in particular, establish strong (pointwise) convergence of the velocities towards a solenoidal vector field.     

Quantum beats in the 3γ annihilation decay of Positronium observed by perturbed angular distribution

We have applied conventional Time Differential Perturbed Angular Correlation (TDPAC) method to observe the anisotropy oscillations in the 3γ annihilation decay of polarized Positronium in a weak magnetic field. The effect, as predicted theoretically and experimentally demonstrated by Barishevsky et al. [V.G. Barishevsky, O.N. Metelitsa, V.V. Tikhomirov, Oscillations of the positronium decay γ-quantum angular distribution in a magnetic field, J. Phys. B: At. Mol. Opt. Phys.22 (1989) 2835], is induced by the coherent admixture of the m = 0 states of ortho-Positronium (o-Ps) and para-Positronium (p-Ps) in interaction with the magnetic field.The following experimental characteristics are to be considered:

(i)

the oscillation frequency corresponds to the difference in energy of the Ps atom levels in magnetic field and is proportional with H²;

(ii)

in a fixed geometry the modulation depth (oscillations amplitude) depends on the mean positron polarization;

(iii)

privileged angles of the polarization vector, magnetic field and detectors are required for optimizing the observed oscillations amplitude.

The normalized difference spectrum function (R(t)) obtained from time spectra measured in vacuum and in different gaseous atmospheres (Ar, H₂, N₂) have the oscillations amplitude constant and we conclude that the Ps atoms are not fully thermalized over a time interval of about 400 ns.The R(t) functions obtained for o-Ps annihilation decays, in dry air or Ar-O mixture, have the oscillations amplitude time dependent due, probably, to the paramagnetism of the Oxygen molecules.     

Defects in the p-n junction and current drift in selenium rectifiers

Drift is considered in relation to a defective p-n junction having localized conduction channels.