Higher differentiability of solutions to variational problems

We prove local higher differentiability of solutions to the problem of minimizing $$\int_\Omega f\left( x, v(x), \nabla v(x)\right) dx$$ under broad assumptions on f.     

Green synthesis and antibacterial activity of chalcogenoesters

Herein, we present a new variation for an eco-friendly methodology for the synthesis of chalcogenoester in good-to-excellent yields in a short time, with an easy work-up/purification step, and in a greenest methodology, affording the minimum generation of solid and liquid waste, in comparison to that described in the literature. Additionally, some selected compounds were evaluated as antimicrobial agents, showing moderate activity against a variety of microorganisms including the K. pneumoniae, P. aeruginosa and also some selected fish pathogenic bacteria.     

Necessary optimality conditions for infinite dimensional state constrained control problems

This paper is concerned with first order necessary optimality conditions for state constrained control problems in separable Banach spaces. Assuming inward pointing conditions on the constraint, we give a simple proof of Pontryagin maximum principle, relying on infinite dimensional neighboring feasible trajectories theorems proved in [20]. Further, we provide sufficient conditions guaranteeing normality of the maximum principle. We work in the abstract semigroup setting, but nevertheless we apply our results to several concrete models involving controlled PDEs. Pointwise state constraints (as positivity of the solutions) are allowed.     

Whispering gallery mode profiles in a coated microsphere

The properties of whispering gallery modes (WGM) of a microsphere can be tailored by coating the resonator with a thin film. If the coating has a higher refractive index than the microsphere core, the resulting structure will have a configuration which has similarities both with a classical WGM resonator and with a planar waveguide. By choosing the film thickness and refractive index we can tailor the degree of confinement of the WGMs inside the sphere core, coating and surrounding medium, which will in turn influence the WGMs contact with its surroundings. We present a study of the effect of the coating on the WGM mode profiles in particular of a silicon coating on a silica sphere.     

Improved yields with added copper(I) salts in carbonylative stille couplings of sterically hindered vinylstannanes

Stille coupling under standard carbonylative conditions proceeds in poor yield when using hindered alkenylstannane and enol triflate partners. The inclusion of 35 mol % CuI or CuBr significantly improves the efficiency of the coupling, providing a variety of complex 1,4-dien-3-ones in good to excellent yield.     

Graph completions for impulsive feedback controls

The paper considers impulsive control systems, where the evolution equation depends linearly on the time derivatives of the control function. The basic theory of “graph completions” is here extended to control functions in feedback form. In the case where the control u=u(t,x)$u=u(t,x)$ is piecewise smooth, with a jump along a hypersurface Σ in the t–x space, results are proved on the existence and uniqueness of solutions, and on their approximation by means of smooth feedbacks. The paper is concluded with a couple of examples, concerning the feedback control of mechanical systems by means of active constraints.     

The bang–bang theorem via Baire category: a dual approach

The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point \({\bar x}\), we consider those which minimize an auxiliary linear functional \({\phi}\). For all \({\phi}\) in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.     

New strategies for the synthesis of partially fluorinated acrylic polymers as possible materials for the protection of stone monuments

The conservation of the cultural heritage requires the development of new materials having specific characteristics that encompass particular attention to durability and efficacy. We approached this problem by synthesizing polyacrylic esters containing variable amounts of fluorine in the α-position of the main chain. These products were obtained from the copolymerisation of ammonium 2-fluoroacrylate and acrylic acid. The polyacrylic acids were esterified using different procedures. The polyester characteristics vary in relation to the polymerisation procedures and degree of esterification. The best esterification results, were obtained using a reaction catalyzed by BF₃ or TMSCl. These materials show good properties and are of potential interest for their use as protective agents for stone conservation.