On the Complexity of SOS Programming and Applications in Control Systems

The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed for real and complex matrix polynomials, in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. Two applications in control systems are presented in order to show the usefulness of the proposed results.     

On the estimation of the domain of attraction for discrete-time switched and hybrid nonlinear systems

This paper addresses the estimation of the domain of attraction for discrete-time nonlinear systems where the vector field is subject to changes. First, the paper considers the case of switched systems, where the vector field is allowed to arbitrarily switch among the elements of a finite family. Second, the paper considers the case of hybrid systems, where the state space is partitioned into several regions described by polynomial inequalities, and the vector field is defined on each region independently from the other ones. In both cases, the problem consists of computing the largest sublevel set of a Lyapunov function included in the domain of attraction. An approach is proposed for solving this problem based on convex programming, which provides a guaranteed inner estimate of the sought sublevel set. The conservatism of the provided estimate can be decreased by increasing the size of the optimisation problem. Some numerical examples illustrate the proposed approach.     

Reliability of a commercial kit to test groundwater for arsenic in Bangladesh

A comparison of field and laboratory measurements of arsenic in groundwater of Araihazar, Bangladesh, indicates that the most widely used field kit correctly determined the status of 88% of 799 wells relative to the local standard of 50 microg/L As. Additional tests showthatthe inconsistencies, mainly underestimates in the 50-100 microg/L As range, can be avoided by increasing the reaction time from 20 to 40 min. Despite this limitation, the field data already compiled for millions of wells by the Bangladesh Arsenic Mitigation and Water Supply Project, in combination with information on well location and depth, should prove to be extremely useful to prioritize interventions in thousands of affected villages.     

Lactation curves of Sarda breed goats estimated with test day models

Test day records of milk yield (38,765), fat and protein contents (11,357) of Sarda goats (the most numerous Italian goat breed) were analysed with mixed linear models in order to estimate the effects of test date (month and year of kidding for fat and protein contents) parity, number of kids born, altitude of location of flocks (<200 m asl, 200-500 m asl, >500 m asl), flocks within altitude and lactation stage (eight days-in-milk intervals of 30 d each) on milk production. All factors considered in the models affected milk traits significantly. Milk yield was lower in first parity goats than in higher parities whereas fat and protein contents showed an opposite trend. Goats with two kids at parturition had a higher milk yield than goats with one kid and tended to have lower fat and protein percentages. Repeatability between test days within lactation was 0.34, 0.17 and 0.45 for milk yield, fat content and protein content, respectively. Lactation curves of goats farmed at different altitudes were clearly separated, especially for milk yield. Results of the present study highlight differences in milk production traits among the three subpopulations that have been previously identified within the Sarda breed on the basis of the morphological structure of animals and altitude of location of flocks.     

Bispecific molecules directed to the Fc receptor for IgA (Fc alpha RI, CD89) and tumor antigens efficiently promote cell-mediated cytotoxicity of tumor targets in whole blood

The FcR for IgA (Fc alpha RI, CD89) is primarily expressed on cytotoxic immune effector cells. By chemically cross-linking F(ab') fragments of the FcR for IgA (Fc alpha RI)-specific mAb (A77) with tumor Ag-specific mAb (anti-HER2/neu and anti-epidermal growth factor receptor), we have developed bispecific molecules (BSM) that simultaneously bind to respective tumor Ags and Fc alpha RI-expressing effector cells in whole blood. These BSM mediated up to 55% of specific lysis of appropriate tumor Ag-expressing target cells (from a variety of tumors) with purified polymorphonuclear leukocytes, monocytes, or whole blood effector cells without preactivation with exogenous cytokines. To our knowledge, this is the first demonstration of Ab-dependent cell-mediated cytotoxic activity via Fc alpha RI in whole blood. Also, monocyte-derived macrophages mediated phagocytosis of HER2/neu-expressing tumor cells (>95% tumor cell loss). These BSM-mediated cytotoxic activities were completely inhibited by F(ab')2 of A77, demonstrating the specific role of Fc alpha RI as a trigger molecule. Furthermore, the binding of these BSM to monocytes or polymorphonuclear leukocytes in whole blood did not induce modulation of Fc alpha RI in the absence of the target Ag. Therefore, immune effector cells may be "armed" with Fc alpha RI-directed BSM in whole blood. These Fc alpha RI-directed BSM may offer new treatment options for various malignancies and other disease conditions.     

Enhancing the mechanical,morphological, and rheological behavior of polyethylene/polypropylene blends with maleic anhydride-grafted polyethylene

This is the first study to showcase the use of maleic anhydride-grafted polyethylene (MAPE) to compatibilize polyethylene (PE)-rich blends, where polypropylene (PP) represents the minor phase. By first mixing PP with MAPE, and then adding PE, MAPE was assumed to be localized at the PE/PP interface. Microscopy analysis confirmed that MAPE led to a remarkably fine PE/PP/MAPE morphology, with PP being uniformly dispersed into PE and having an average diameter 267% smaller than that in the PE/PP blend. According to mechanical and rheological tests, this translated into a 14%, 20%, and 14% enhancement of tensile strength, tensile modulus, and tensile toughness, respectively, as well as a 10% and 20% drop in PE/PP viscosity mismatch and interfacial tension, respectively. Finally, PE/PP/MAPE tensile toughness and elongation at break were greater than those of virgin PP, while PE/PP/MAPE strength and stiffness were similar to the ones of neat PP. Therefore, this study provides industries with the possibility to utilize products rich in PE instead of those made of more expensive PP, while still keeping the level of performance high; hence, creating a paradigm shift in the development of advanced lightweight polyolefin materials with tuned functionalities.     

Friction and wear behaviour of sintered steels submitted to sliding and abrasion tests

Fe–C–Mo and Fe–C–Cr steels were sintered by PM processes carried out using different values of temperature and pressure, leading to different microstructures and density values. Flat specimens were submitted to tribological tests in order to evaluate their behaviour under both dry sliding and abrasive wear conditions. A flat-on-cylinder tribometer was used for the sliding tests, while a micro-scale ball cratering device was used for the abrasion tests. The dry sliding wear resistance of the PM steels was mainly influenced by the composition and sintering conditions. In this regard, the best behavior was observed for the more hardenable Fe–C–Mo steels with higher Mo content, sintered under conditions giving rise to bainitic microstructures. A determining role was also played by the porosity content and pore shape: reduction in porosity (obtained by increasing the sintering temperature and the compacting pressure), as well as an increase in pore roundness, led to a significant improvement in the resistance to sliding wear. A mild oxidative wear regime were observed for all the sintered steels under relatively low values of the applied load, while an increase of the applied load led to a delamination wear regime. The resistance to abrasive wear was low for all the tested steels, irrespective of composition and sintering cycle.     

Road safety issues for bus transport management

Because of the low percentage of crashes involving buses and the assumption that public transport improves road safety by reducing vehicular traffic, public interest in bus safety is not as great as that in the safety of other types of vehicles. It is possible that less attention is paid to the significance of crashes involving buses because the safety level of bus systems is considered to be adequate.     

Time-Dependent Analysis of Shear-Lag Effect in Composite Beams

Taking into account the long-term behavior of the concrete, a model for analyzing the shear-lag effect in composite beams with flexible shear connection is proposed. By assuming the slab loss of planarity described by a fixed warping function, the linear kinematics of the composite beam is expressed by means of four unknown functions: the vertical displacement of the whole cross section; the axial displacements of the concrete slab and of the steel beam; and the intensity of the warping (shear-lag function). A variational balance condition is imposed by the virtual work theorem for three-dimensional bodies, from which the local formulation of the problem, which involves four equilibrium equations with the relevant boundary conditions, is achieved. The assumptions of linear elastic behavior for the steel beam and the shear connection and of linear viscoelastic behavior for the concrete slab lead to an integral-differential type system, which is numerically integrated. The numerical procedure, based on the step-by-step general method and the finite-difference method, is illustrated and applied to an example of practical interest.