Linear stability of the spatially homogeneous equilibria of the Vlasov-Poisson system with collisions

In this work we study the stability of the spatially homogeneous solutions of the Vlasov-Poisson system (Vlasov equilibria) when a collision term, in the form of a BGK operator with velocity-dependent collision frequency, is added to the Vlasov equation. Generalizing earlier results, obtained for the same collision model with a constant collision frequency, we find the spectrum and the eigenfunctions of the linear transport operator and derive a new linear dispersion relation for the linearized kinetic equations. Finally, we present some numerical results.     

Algebraic spinors and SUSY

Using the Dirac-Kaehler formalism, we formulate the supersymmetric Wess-Zumino model. Special attention is paid to the proper definition of a two-dimensional spinor, its adjoint, and its generalization to other dimensions.     

A biogenetically new tetraterpene alcohol from elodea canadensis

On the basis of spectroscopic data structure 1 is proposed for a tetraterpene alcohol isolated from Elodea canadensis. A new biogenetic route is suggested for its formation.     

Estimates on path delocalization for copolymers at selective interfaces

Starting from the simple symmetric random walk {S_n}_n, we introduce a new process whose path measure is weighted by a factor exp with α,h≥0, {W_n}_n a typical realization of an IID process and N a positive integer. We are looking for results in the large N limit. This factor favors S_n>0 if W_n+h>0 and S_n<0 if W_n+h<0. The process can be interpreted as a model for a random heterogeneous polymer in the proximity of an interface separating two selective solvents. It has been shown [6] that this model undergoes a (de)localization transition: more precisely there exists a continuous increasing function λ↦h_c(λ) such that if h<h_c(λ) then the model is localized while it is delocalized if h≥h_c(λ). However, localization and delocalization were not given in terms of path properties, but in a free energy sense. Later on it has been shown that free energy localization does indeed correspond to a (strong) form of path localization [3]. On the other hand, only weak results on the delocalized regime have been known so far. We present a method, based on concentration bounds on suitably restricted partition functions, that yields much stronger results on the path behavior in the interior of the delocalized region, that is for h>h_c(λ). In particular we prove that, in a suitable sense, one cannot expect more than O( log N) visits of the walk to the lower half plane. The previously known bound was o(N). Stronger O(1)–type results are obtained deep inside the delocalized region. The same approach is also helpful for a different type of question: we prove in fact that the limit as α tends to zero of h_c(λ)/λ exists and it is independent of the law of ω₁, at least when the random variable ω₁ is bounded or it is Gaussian. This is achieved by interpolating between this class of variables and the particular case of ω₁ taking values ±1 with probability 1/2, treated in [6].     

Stereochemistry of cercosporin

The absolute configuration of the asymmetric carbons and the axial chirality of the natural mold metabolite cercosporin (from $\text{Cercospora sp}$.) have been established on the basis of X-ray analysis and chemical reactions. The results confirm the inherent dissymmetry of the perylenequinone ring, the twisting of which gives rise to the diastereoisomer isocercosporin. The energy barrier for the conversion of cercosporin into isocercosporin has been evaluated.     

Stabilità delle soluzioni di disequazioni variazionali ellittiche e paraboliche quasi lineari

Riassunto In questo lavoro, si studia, per una classe di operatori quasi-lineari, il problema della dipendenza simultanea dai vincoli, dai coefficienti dell'operatore e dai termini noti delle soluzioni di disequazioni variazionali ellittiche e delle soluzioni forti di disequazioni variazionali paraboliche. L'esistenza di queste ultime è consequenza dei risultati precedenti.

---

Summary We study the problem of the dependence from the data of the solutions of quasilinear elliptic variational inequalities. We also consider the case of the strong solutions of parabolic variational inequalities, whose existence has been proved as a consequence of the previous results.

---

---

Lavoro eseguito nell'ambito del G.N.A.F.A.—C.N.R.     

A structure of the Bang-Bang representation for 3×3 embeddable matrices

Summary Necessary and sufficient conditions are given for a 3×3 stochastic matrix to be embeddable by 6 elementary stochastic matrices (Poisson matrices). For a 3×3 embeddable matrix, a structure of the minimal Bang-Bang representation, i.e. the one that contains the smallest number of elementary matrices, is obtained. Based on the minimal Bang-Bang representation an algorithm for determining the embeddability of a 3×3 stochastic matrix is given.I would like to thank Søren Johansen for helpful comments and stimulating discussions on the subject of this paper     

Phenomenology of a second neutral gauge boson in the Drell-Yan process

We discuss the influence of a second neutral gauge boson to the Drell-Yan process. We find that for energies available in the near future and even at present energies, there are sizeable differences in the predictions of different models for the forward-backward asymmetry and the longitudinal polarization of the lepton.