Extending Bauer's corollary to fractional derivatives

We comment on the method of Dreisigmeyer and Young [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems with fractional derivatives. It was previously hoped that using fractional derivatives in an action would allow us to derive a single retarded equation of motion using a variational principle. It is proven that, under certain reasonable assumptions, the method of Dreisigmeyer and Young fails.Comment: Accepted Journal of Physics A at www.iop.org/EJ/journal/JPhys

Nonconservative Lagrangian mechanics II: purely causal equations of motion

This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle

A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Determination of deoxynivalenol and nivalenol producing chemotypes of Fusarium graminearum isolated from durum wheat in different Italian regions

Durum wheat production in Italy is economically of great importance. Fusarium graminearum is the main fusarium head blight (FHB) causal agent in wheat, reducing both yield and grain quality. F. graminearum produces several mycotoxins and, among trichothecenes, deoxynivalenol (DON) and nivalenol (NIV) are the most studied for their toxicity towards humans and animals. DON-producing isolates can be further distinguished on the basis of the predominant acetyl-DON derivative in 3-acetyldeoxynivalenol (3-ADON) or 15acetyldeoxynivalenol (15-ADON). In order to evaluate possible mycotoxin contamination risks in food, it is very important to know which chemotype is the prevalent in a F. graminearum population. F. graminearum sensu stricto strains were collected from symptomatic durum wheat heads and grains of several naturally infected fields located mostly in Emilia – Romagna, The Marche, Lazio, Tuscany and Umbria. A multiplex PCR in the region of genes Tri12, located in the terminal gene cluster of trichothecenes, was used to characterize 187 single-spore isolates of F. graminearum as NIV, 3-ADON and 15-ADON chemotypes. All the three chemotypes were present in the F. graminearum population studied. The most frequent chemotype was 15-ADON (83.4%), followed by 3-ADON (10.7%) and NIV (5.9%). NIV-producing isolates were found only in Emilia-Romagna (3.5%), Umbria (33.3%) and The Marche (5.7%)