Mechanically-based approach to non-local elasticity: Variational principles

The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Moreover, the Euler–Lagrange equations together with the natural boundary conditions associated to the total potential energy functional are established with variational calculus and they coincide with analogous relations already obtained by means of mechanical considerations. Numerical analysis of a tensile specimen has been introduced to show the capabilities of the proposed approach.     

A dynamic model for road protection against flooding

This paper focuses on the problem of identifying optimal protection strategies to reduce the impact of flooding on a road network. We propose a dynamic mixed-integer programming model that extends the classic concept of road network protection by shifting away from single-arc fortifications to a more general and realistic approach involving protection plans that cover multiple components. We also consider multiple disruption scenarios of varying magnitude. To efficiently solve large problem instances, we introduce a customised GRASP heuristic. Finally, we provide some analysis and insights from a case study of the Hertfordshire road network in the East of England. Results show that optimal protection strategies mainly involve safeguarding against flooding events that are small and likely to occur, whereas implementing higher protection standards are not considered cost-effective.     

Subexpansions,superexpansions and uniqueness properties in non-integer bases

The β-expansions, i.e., greedy expansions with respect to non-integer bases q>1, were introduced by Réenyi and then investigated by many authors. Some years ago, Erdős, Horváth and Joó found the surprising fact that there exist infinitely many numbers 1<q<2 for which the β-expansion of 1 is the unique possible expansion with coefficients 0 or 1. Subsequently, the unique expansions were characterized in [9] and this characterization led to the determination (in [17]) of the smallest number q having this curious property. It is intimately related to the classical Thue-Morse sequence. Allouche and Cosnard recently proved that this q is transcendental. The purpose of this paper is to extend the previous results for expansions in arbitrary non-integer bases q>1. We also determine the smallest q having the corresponding uniqueness property in each case, and we prove that all of them are transcendental. We will also obtain some probably new properties of the Thue-Morse sequence. In the last section we answer a question concerning the existence of universal expansions, a notion introduced in [12]. This revised version was published online in June 2006 with corrections to the Cover Date.     

Degradation of imazosulfuron in different soils-HPLC determination

Imazosulfuron, 1-(2-chloroimidazo [1,2-a] pyridin-3-ylsulfonyl)-3-(4,6-dimethoxypyrimidin-2-yl)urea, is a new sulfonylurea herbicide applied once per growing season. It is highly active at low application levels and is used to control most annual and perennial broad-leaf weeds and some grasses in cereal crop. In this work the degradation of imazosulfuron in four different soils was investigated under aerobic laboratory conditions to evaluate its environmental fate. Test soils were treated with this herbicide in acetonitrile to obtain a final concentration of 0.2 mg kg(-1) (100 g ha(-1)), extracted with methylene chloride and analyzed by reversed-phase liquid chromatography (RP-HPLC) using a C(18) column coupled with UV detection. Recoveries of spiked soils ranged from 84.3 to 99.8% (RDS 0.0-4.9%; n = 4). The limits of quantitation ranged from 0.002 to 0.004 mg kg(-1). Imazosulfuron half-life, t(1/2), was calculated in each of the investigated soil. In aerobic conditions it ranged between 1 and 50 days.     

Trimethoxysilylpolymethacrylate as new material for stone conservation. Porosimetric and colorimetric investigations

Aimed to obtain new materials for the conservation of stone substrates, we report here on the synthesis of a polymer which has been obtained by inducing polymerization on a methacrylate monomer functionalized by alchoxysilane groups. Two lithotypes, the Comiso calcarenite and Mistretta quartzite, stones largely used in artworks of north-eastern Sicily, were treated with the above polymer and its conserving efficacy evaluated in terms of porosimetric features, hydric properties and appearance. The collected data were compared to those provided, under the same experimental conditions, by an ethylmethacrylate/methylmethacrylate copolymer and an alkylalchoxysilane, products widely employed in the protection of stones. Experiments aimed to test the durability of the above polymer against UV artificial ageing are also reported.     

Determination of the acid dissociation constant of bromocresol green and cresol red in water/AOT/isooctane reverse micelles by multiple linear regression and extended principal component analysis

The pKa of 3',3",5',5"tetrabromo-m-cresolsulfonephtalein (Bromocresol Green) and o-cresolsulphonephtalein (Cresol Red) was spectrophotometrically measured in a water/AOT/isooctane microemulsion in the presence of a series of buffers carrying different charges at different water/surfactant ratios. Extended Principal Component Analysis was used for a precise determination of the apparent pKa and of the spectra of the acid and base forms of the dye. The apparent pKa of dyes in water-in-oil microemulsions depends on the charge of the acid and base forms of the buffers present in the water pool. Combination with multiple linear regression increases the precision. Results are discussed taking into account the profile of the electrostatic potential in the water pool and the possible partition of the indicator between the aqueous core and the surfactant. The pKa corrected for these effects are independent of w0 and are close to the value of the pKa in bulk water. On the basis of a tentative hypothesis it is possible to calculate the true pKa of the buffer in the pool.     

High-performance liquid chromatographic/tandem mass spectrometric identification of the phototransformation products of tebuconazole on titanium dioxide

Tebuconazole is a widely used fungicide. The formation of by-products on irradiated titanium dioxide as a photocatalyst was evaluated. Several species derived from tebuconazole degradation were identified and characterized by HPLC/MS(n). A pattern of reactions accounting for the observed intermediates is proposed. Different parallel pathways are operating (and through these pathways the transformation of the molecule proceeds), leading to a wide range of intermediate compounds. All these molecules are more hydrophylic than tebuconazole. The main steps involved are (1) the hydroxylation of the molecule with the formation of three species having [M + H](+) 324; the hydroxylation occurs on the C-1 carbon and on the aromatic ring in the two ortho-positions; (2) the cleavage of a C--C bond with the release of the tert-butyl moiety and the formation of a species having m/z 250; analogously to step 1, also on this species a further hydroxylation reaction occurs; (3) through the loss of the triazole moiety with the formation of a structure with m/z 257.