Some estimates for the weakly convergent sequence coefficient in Banach spaces

We present relations between the weakly convergent sequence coefficient of a Banach space and other coefficients. Some estimates are sharp.     

Decidability of the word problem in Yamamura’s HNN extensions of finite inverse semigroups

We prove that the word problem is decidable in Yamamura’s HNN extensions of finite inverse semigroups, by providing an iterative construction of approximate automata of the Schützenberger automata of words relative to the standard presentation of Yamamura’s HNN-extensions. This work was done in the framework of the group GNSAGA of INDAM, the PRIN “Automi e Linguaggi Formali: aspetti matematici e applicativi” and the ESF project Automatha.     

A General Method for the Preparation of 2,2,4-Trimethyl and 2,2-Dimethyl-4-Isophopyl-6-Hydhoxy-7-Substituted Cheomans

2,2,4-Trimethyl and 2,2-dimethyl-4-isopropyl-6-hydroxy-7-substituted chromans can be conveniently prepared by the reaction of 2-substituted hydroquinones with 2-methyl-2,4-pentanediol or 2,5-diraethyl-2,5-hexanediol, respectively, in the presence of macroreticular strongly acidic sulfonic acid cation exchange resin catalysts. The reaction is positionally selective and allows for simple workups and reasonable yields.     

Parallel dedicated machines scheduling with chain precedence constraints

A set of n nonpreemptive tasks are to be scheduled on m parallel dedicated machines with a regular criterion. Chain precedence constraints among the tasks, deterministic processing times and processing machine of each task are given.     

Groups whose nonlinear irreducible characters separate element orders or conjugacy class sizes

A class function φ on a finite group G is said to be an order separator if, for every x and y in G \ {1}, φ(x) = φ(y) is equivalent to x and y being of the same order. Similarly, φ is said to be a class-size separator if, for every x and y in G\ {1}, φ(x) = φ(y) is equivalent to |C _G (x)| = |C _G (y)|. In this paper, finite groups whose nonlinear irreducible complex characters are all order separators (respectively, class-size separators) are classified. In fact, a more general setting is studied, from which these classifications follow. This analysis has some connections with the study of finite groups such that every two elements lying in distinct conjugacy classes have distinct orders, or, respectively, in which disctinct conjugacy classes have distinct sizes. Received: 10 April 2007     

On the Propagation of a Perturbation in an Anharmonic System

We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.     

FT-ICR-MS analysis of lignin

Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) of a steam-exploded lignin from wheat straw showed that fragments with a mass higher than 4534?Da cannot be obtained. Furthermore, FT-ICR-MS showed that lignin is not a completely random polymer, but shows some regularity with a difference of 44.026?m/z (C?H?O) between the peaks. The distribution of Kendrick mass defect in the function of Kendrick nominal masses showed the same behaviour. FT-ICR-MS analysis of bagasse lignin (Granit) showed that the largest value of mass found was 4347?Da. The peaks show regularities with a difference of 44.026?m/z between the peaks. The organosolv lignin showed that the polymer with the largest mass value was 3699?Da in FT-ICR-MS. The analysis of the peaks did not show regularity; however, the Kendrick diagram for this lignin showed the same slope as in the other samples, in agreement with the C?H?O regular difference between peaks.     

Fixed points of endomorphisms of trace monoids

It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. If the dependence alphabet is a transitive forest, it is proved that the set of regular fixed points of the (Scott) continuous extension of an endomorphism to real traces is Ω-rational for every endomorphism if and only if the monoid is a free product of free commutative monoids.     

Order Reduction of General Nonlinear DAE Systems by Automatic Tearing

The object-oriented approach to modelling has recently made possible to build models of large-scale real systems. However, the resulting system of equations is generally a nonlinear DAE (Differential Algebraic Equations) system of large dimension, which must be reduced in some way to make it tractable for numerical solutions. A way to do this is automatic symbolic tearing, which aims at splitting the DAE system into two parts: a core consisting of a reduced implicit DAE system and a set of explicit assignments. The problem is here dealt with by a graph theoretic approach, first proving the NP-completeness in the general case, then formulating the problem with reference to a bipartite graph and finally defining an efficient and flexible algorithm for automatic tearing. It is also shown how the proposed algorithm can easily incorporate both general and domain-specific heuristic rules, and can also be used to deal with equations in vector form. The application to serial multibody systems is considered as a significant example.