Cubature formulae for nearly singular and highly oscillating integrals

The paper deals with the approximation of integrals of the type

$$\begin{aligned} I(f;{\mathbf {t}})=\int _{{\mathrm {D}}} f({\mathbf {x}}) {\mathbf {K}}({\mathbf {x}},{\mathbf {t}}) {\mathbf {w}}({\mathbf {x}}) d{\mathbf {x}},\quad \quad {\mathbf {x}}=(x_1,x_2),\quad {\mathbf {t}}\in \mathrm {T}\subseteq \mathbb {R}^p, \ p\in \{1,2\} \end{aligned}$$

where \({\mathrm {D}}=[-\,1,1]^2\), f is a function defined on \({\mathrm {D}}\) with possible algebraic singularities on \(\partial {\mathrm {D}}\), \({\mathbf {w}}\) is the product of two Jacobi weight functions, and the kernel \({\mathbf {K}}\) can be of different kinds. We propose two cubature rules determining conditions under which the rules are stable and convergent. Along the paper we diffusely treat the numerical approximation for kernels which can be nearly singular and/or highly oscillating, by using a bivariate dilation technique. Some numerical examples which confirm the theoretical estimates are also proposed.

     

Reactive mixing of PET and PET/PP blends with glycidyl methacrylate–modified styrene‐b‐(ethylene‐co‐olefin) block copolymers

Styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene (SEBS) and styrene‐b‐(ethylene‐co‐propylene) (SEP, SEPSEP) block copolymers with different styrene contents and different numbers of blocks in the copolymer chain were functionalized by melt radical grafting with glycidyl methacrylate (GMA) and employed as compatibilizers for PET‐based blends. Binary blends of PET with both functionalized (SEBS‐g‐GMA, SEP‐g‐GMA, SEPSEP‐g‐GMA) and neat (SEBS, SEP, SEPSEP) copolymers (75 : 25 w/w) and ternary blends of PET and PP (75 : 25 w/w) with various amounts (2.5–10 phr) of both modified and unmodified copolymers were prepared in an internal mixer, and their properties were evaluated by SEM, DSC, melt viscosimetry, and tensile and impact tests. The roles of the chemical structure, grafting degree, and concentration of the various copolymers on blend compatibilization was investigated. The blends with the grafted copolymers showed a neat improvement of phase dispersion and interfacial adhesion compared to the blends with nonfunctionalized copolymers. The addition of grafted copolymers resulted in a marked increase in melt viscosity, which was accounted for by the occurrence of chemical reactions between the epoxide groups of GMA and the carboxyl/hydroxyl end groups of PET during melt mixing. Blends with SEPSEP‐g‐GMA and SEBS‐g‐GMA, at concentrations of 5–10 phr, showed a higher compatibilizing effect with enhanced elongation at break and impact resistance. The effectiveness of GMA‐functionalized SEBS was then compared to that of maleic anhydride–grafted SEBS. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 2201–2211, 2005     

A unifying framework for ℓ 0-sampling algorithms

The problem of building an ? ₀-sampler is to sample near-uniformly from the support set of a dynamic multiset. This problem has a variety of applications within data analysis, computational geometry and graph algorithms. In this paper, we abstract a set of steps for building an ? ₀-sampler, based on sampling, recovery and selection. We analyze the implementation of an ? ₀-sampler within this framework, and show how prior constructions of ? ₀-samplers can all be expressed in terms of these steps. Our experimental contribution is to provide a first detailed study of the accuracy and computational cost of ? ₀-samplers.     

A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem

In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is $H(\mathrm{div},\Omega )$ -conforming. This implies that the velocity solution is divergence-free in the whole domain. This property can be exploited to design a simple and effective preconditioner for the final linear system.     

A vision system for symbolic interpretation of dynamic scenes using arsom

We describe an artificial high-level vision system for the symbolic interpretation of data coming from a video camera that acquires the image sequences of moving scenes. The system is based on ARSOM neural networks that learn to generate the perception-grounded predicates obtained by image sequences. The ARSOM neural networks also provide a three-dimensional estimation of the movements of the relevant objects in the scene. The vision system has been employed in two scenarios: the monitoring of a robotic arm suitable for space operations, and the surveillance of an electronic data processing (EDP) center.     

Allergenicity of different apple cultivars assessed by means of skin prick test and sensitisation to recombinant allergens Mal d 1 and Mal d 3 in a group of Italian apple‐allergic patients

To evaluate differences in skin prick test response to apple cultivars in patients with apple allergy, 19 patients (10 adults and 9 children) underwent prick‐to‐prick skin prick test with eleven commercial and noncommercial apple cultivars, and evaluation of specific IgE to apple and recombinant apple allergens Mal d 1 and Mal d 3. The results show that different reactions might be evoked in a single patient by different apple cultivars and also separately for the peel and the pulp of a single cultivar. The cultivars were ranked according to their allergenicity level, being Jonathan, Jonagold, Golden Delicious and Fiesta the most allergenic when considering the pulp and Gala, Fiesta and Golden Delicious for the peel. Further investigations are needed to clarify if a single patient can be allergic only to well‐defined apple cultivars and which allergometric tests are necessary to ascertain this.     

HPLC-Chip-Multiple Reaction Monitoring (MRM) method for the label-free absolute quantification of γ-conglutin in lupin: Proteotypic peptides and standard addition method

In food science there is a growing demand of methods for the absolute quantification of proteins, such as allergens or bioactive proteins, and shotgun proteomics based on mass spectrometry is a promising analytical tool in this area. This paper describes an innovative label-free method for the absolute quantification of γ-conglutin, one of the most relevant lupin seed proteins, which is hypoglycaemic and a major allergen. The main features of the method are: (a) the chromatographic separation was performed on an HPLC-chip system coupled with an ion trap mass spectrometer; (b) five proteotypic peptides of γ-conglutin were selected and analysed with a multiple reaction monitoring (MRM) method; (c) absolute quantification was obtained by the standard addition method after purification of a reference sample of γ-conglutin from lupin seed; (d) the matrix effect was overcome by spiking with an exogenous protein, i.e. BSA, as internal standard.     

The effect of chain packing on the thermal and dynamic mechanical behaviour of liquid‐crystalline epoxy thermosets

Liquid‐crystalline thermosets (LCTs) have received considerable attention since they exhibit many interesting properties. However, some aspects concerning LCTs are still unexplored. In particular, the structure–property relationships, as far as the organization of liquid‐crystalline (LC) domains in cured thermosets is concerned, have not been fully elucidated yet. We investigated the effect of the presence of a nematic mesophase on the thermal and dynamic mechanical behaviour of p‐(2,3‐epoxypropoxy)phenyl‐p‐(2,3‐epoxypropoxy)benzoate cured with 2,4‐diaminotoluene. Fourier transform infrared spectral analysis showed that epoxy group conversion was complete in both LC and isotropic (ISO) systems; moreover, a greater amount of intermolecular hydrogen bonding in the LC material was found. Thermogravimetric analysis evidenced similar thermal stability for the two systems, but a kinetic analysis of the data showed that the degradation process is more complex for the LC sample, and is characterized by higher activation energy. Dynamic mechanical thermal analysis (DMTA) showed lower glass transition temperature values for the LC system. Solid‐state NMR analysis evidenced lower paramagnetic oxygen absorption for this system. DMTA results show that the ISO material possesses a larger number of physical crosslinks, which act as extra constraints on the molecular motions. In the case of the LCT, the formation of a locally more dense structure is postulated, where the presence of more extended macromolecular segments leads to a smaller number of physical crosslinks, as also confirmed by solid‐state NMR analysis. A more compact molecular packing also leads to an increase of the activation energies of the thermal degradation process of the LC system. Copyright © 2010 Society of Chemical Industry     

Technological properties and non-enzymatic browning of white lupin protein enriched spaghetti

Spaghetti was prepared by replacing semolina with different amounts of lupin protein, in order to increase the protein content. A detailed investigation of the rheological properties of the dough and the cooking quality of pasta was performed in comparison to standard semolina spaghetti. Moreover, the effect of the addition of lupin protein on non-enzymatic browning was evaluated by measuring ε-furoylmethyllysine (furosine) and 5-hydroxymethyl-2-furancarboxaldehyde (HMF), which are considered useful indices of semolina quality and pasta processing conditions. Dried spaghetti fortified with 5% of lupin protein isolate has a colour and rheological features comparable with the semolina sample and also the behaviour during cooking results to be satisfactory. As far as the thermal damage is concerned, the furosine values of fortified spaghetti differ only marginally from standard pasta and the percentage lysine loss is quite small (ranging from 12.1% to 15.7%).