A monomial cycle basis on Koszul homology modules

We give a class of p-Borel principal ideals of a polynomial algebra over a field K for which the graded Betti numbers do not depend on the characteristic of K and the Koszul homology modules have a monomial cyclic basis.     

The second Brauer-Thrall conjecture for isolated singularities of excellent hypersurfaces

We give an extension of Dieterich's Theorems on the structure of the Auslander-Reiten quiver of an isolated singularity. The first author was supported by a fellowship of the Alexander von Humboldt-Stiftung during the last period of preparation of this paper.     

Quasistatic Evolution in Debonding Problems via Capacitary Methods

We discuss quasistatic evolution processes for capacitary measures and shapes in order to model debonding membranes. Minimizing movements as well as rate-independent processes are investigated and some models are described, together with a series of open problems.     

Three-dimensional numerical simulation of the reciprocating flow in a branching tube network

The paper deals with the three dimensional numerical simulation of the reciprocating flow in a branching network, a phenomenon that might be found for example in the human bronchi. As the first approximation, the working fluid was water with laminar flow regime. The main issue was to elucidate the mechanism of the air exchange in the human lungs. The model used in this simulation consists of two branching generations. Three different cases have been analyzed with various frequency, Re and Wo numbers.     

Duality Questions for Operators,Spectrum and Measures

We explore spectral duality in the context of measures in ℝ ⁿ , starting with partial differential operators and Fuglede’s question (1974) about the relationship between orthogonal bases of complex exponentials in L ²(Ω) and tiling properties of Ω, then continuing with affine iterated function systems. We review results in the literature from 1974 up to the present, and we relate them to a general framework for spectral duality for pairs of Borel measures in ℝ ⁿ , formulated first by Jorgensen and Pedersen.     

Monotonicity Formula and Regularity for General Free Discontinuity Problems

We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d ? 1. This result allows us to prove partial regularity results (that is closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi–Carriero–Leaci result for the Mumford–Shah functional.     

A Variational Approach to the Isoperimetric Inequality for the Robin Eigenvalue Problem

The isoperimetric inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions was recently proved by Daners in the context of Lipschitz sets. This paper introduces a new approach to the isoperimetric inequality, based on the theory of special functions of bounded variation (SBV). We extend the notion of the first eigenvalue λ₁ for general domains with finite volume (possibly unbounded and with irregular boundary), and we prove that the balls are the unique minimizers of λ₁ among domains with prescribed volume.     

Ordered mesoporous silicon carbide (OM-SiC) via polymer precursor nanocasting

Ordered mesoporous SiC with high specific surface area (650-800 m(2) g(-1)) and well ordered pore structure was obtained via nanocasting of polycarbosilanes into SBA-15 and subsequent conversion of the polymer at 1300 degrees C.