Some people and places important in the history of analytical chemistry in Italy

The people and places of importance to the history of chemistry in Italy have been reviewed with particular reference to Analytical Chemistry. Correspondence: D. Thorburn Burns, The Science Library, The Queen’s University of Belfast, Belfast BT9 5EQ, Northern Ireland     

Some remarks on the Minty vector variational principle

In scalar optimization it is well known that a solution of a Minty variational inequality of differential type is a solution of the related optimization problem. This relation is known as “Minty variational principle.” In the vector case, the links between Minty variational inequalities and vector optimization problems were investigated in [F. Giannessi, On Minty variational principle, in: New Trends in Mathematical Programming, Kluwer Academic, Dordrecht, 1997, pp. 93-99] and subsequently in [X.M. Yang, X.Q. Yang, K.L. Teo, Some remarks on the Minty vector variational inequality, J. Optim. Theory Appl. 121 (2004) 193-201]. In these papers, in the particular case of a differentiable objective function f taking values in Rm and a Pareto ordering cone, it has been shown that the vector Minty variational principle holds for pseudoconvex functions. In this paper we extend such results to the case of an arbitrary ordering cone and a nondifferentiable objective function, distinguishing two different kinds of solutions of a vector optimization problem, namely ideal (or absolute) efficient points and weakly efficient points. Further, we point out that in the vector case, the Minty variational principle cannot be extended to quasiconvex functions.     

Multidimensional continued fractions and a Minkowski function

The Minkowski question mark function can be characterized as the unique homeomorphism of the real unit interval that conjugates the Farey map with the tent map. We construct an n-dimensional analogue of the Minkowski function as the only homeomorphism of an n-simplex that conjugates the piecewise-fractional map associated to the M?nkemeyer continued fraction algorithm with an appropriate tent map. Author’s address: Department of Mathematics, University of Udine, via delle Scienze 208, 33100 Udine, Italy     

Penkvilksite‐2O: Na2TiSi4O11·2H2O

The crystal structure of synthetic penkvilksite‐2O, disodium titanium tetrasilicate dihydrate, Na₂TiSi₄O₁₁·2H₂O, a microporous titanosilicate, confirms the major features of a previous model that had been obtained by order–disorder (OD) theory from the known structure of penkvilksite‐1M. An important difference from the previous model involves the hydrogen bonding of the water molecule which, on the basis of a Raman spectrum and the finding of only one of the two H atoms, is proposed to be disordered about a fixed O–H direction. The structure of penkvilksite‐2O is based on (100) silicate layers linked by isolated TiO₆ octahedra to form a heteropolyhedral framework. The layer is strongly corrugated, based on interlaced spiral chains, and is crossed by two different channels that have an effective channel width of about 3 Å.     

Counting Phase Space Cells in Statistical Mechanics

The problem of counting the number of phase space cells is analyzed with the purpose of interpreting the variational principle for the SRB statistics as an equidistribution property, in equilibrium as well as in nonequilibrium statistical mechanics. Received: 16 November 2000 / Accepted: 22 April 2001     

Quasinormal subgroups of order p 2

The location of quasinormal subgroups in a group is not particularly well known. Maximal ones always have to be normal, but little has been proved about the minimal ones. In finite groups, the difficulties arise in the p-groups. Here we prove that, for every odd prime p, a quasinormal subgroup of order p ² in a finite p-group G contains a quasinormal subgroup of G of order p. S. Stonehewer is grateful to the Australian National University for financial support during the preparation of this paper.     

Projection of diffusions on submanifolds: Application to mean force computation

We consider the problem of sampling a Boltzmann‐Gibbs probability distribution when this distribution is restricted (in some suitable sense) on a submanifold Σ of ?ⁿ implicitly defined by N constraints q₁(x) = ? = q_N(x) = 0 (N < n). This problem arises, for example, in systems subject to hard constraints or in the context of free energy calculations. We prove that the constrained stochastic differential equations (i.e., diffusions) proposed in [7, 13] are ergodic with respect to this restricted distribution. We also construct numerical schemes for the integration of the constrained diffusions. Finally, we show how these schemes can be used to compute the gradient of the free energy associated with the constraints. © 2007 Wiley Periodicals, Inc.     

Studies of poly(vinylidene fluoride)/poly(vinyl pyrrolidone) blends. I. Thermal transitions by differential scanning calorimetry

Thermal measurements were carried out to investigate the macrostructure of as-cast poly(vinylidene fluoride) (PVDF)/poly(vinyl pyrrolidone) (PVP) blends. At high PVP content, above about 70 wt.%, the two components form a homogeneously mixed amorphous phase whose T_g varies with composition. Crystals are formed upon casting mixtures richer in PVDF; these systems exhibit complex thermal behavior that cannot be justified by a simple two-phase model. DSC measurements above room temperature on semicrystalline blends show, in addition to the melting of PVDF crystals at temperatures that decrease on increasing PVP content, a glass transition at about 80°C, independent of composition. Experimental results strongly support the hypothesis that an interphase, composed of essentially undiluted noncrystalline PVDF, is always associated with the lamellar crystals.     

Optimization models for the single delay management problem in public transportation

Passengers travelling in public transportation networks often have to use different lines to cover the trip from their origin to the desired destination. As a consequence, the reliability of connections between vehicles is a key issue for the attractiveness of the intermodal transportation network and it is strongly affected by some unpredictable events like breakdowns or vehicle delays. In such cases, a decision is required to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The delay management problem (DMP) consists in defining the wait/depart policy which minimizes the total delay on the network. In this work, we present two equivalent mixed integer linear programming models for the DMP with a single initial delay, able to reduce the number of variables with respect to the formulations proposed by the literature. The two models are solved by a branch and cut procedure and by a constraint generation approach respectively, and preliminary computational results are presented.