Classical and non-classical solutions of a prescribed curvature equation

We discuss existence and multiplicity of positive solutions of the one-dimensional prescribed curvature problem

depending on the behaviour at the origin and at infinity of the potential . Besides solutions in W^2,1(0,1), we also consider solutions in which are possibly discontinuous at the endpoints of [0,1]. Our approach is essentially variational and is based on a regularization of the action functional associated with the curvature problem.     

Dynamic switching between binding sites in the complexation of macrocyclic ‘push-pull’ chromophores to lanthanides

The introduction of a 1,3-diacetylpyridine moiety, as an additional binding niche in a macrocyclic receptor ligand containing a conjugated, push-pull malonate functionality, leads to, in addition to the 1:1 binding stoichiometry, the equilibrium formation of multiple complexes, specifically 1:2, 2:1, and 3:1 ligand:metal complexes with lanthanide trications. Various binding modes elicit distinctive responses in the visible region, which enhance the potential recognition of lanthanide ions. This paper also highlights the usefulness of a full factor analysis in the elucidation of complex binding phenomena.     

Degenerate elliptic equations with singular nonlinearities

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of , and compactness holds below a critical dimension N ^#. The nonlinearity f(u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p ≠ 2 it is crucial to define a suitable notion of semi-stability: the functional space we introduce in the paper seems to be the natural one and yields to a spectral theory for the linearized operator. For the case p = 2, compactness is also established along unstable branches satisfying suitable spectral information. The analysis is based on a blow-up argument and stronger assumptions on the nonlinearity f(u) are required. Authors are partially supported by MIUR, project “Variational methods and nonlinear differential equations”.     

A comparison of different semi-analytical techniques to determine the nonlinear oscillations of a slender microbeam

The purpose of this work is to investigate the dynamic behaviour of an electrically-actuated microbeam. The electromechanical model is based on the strain-gradient elasticity theory and it gives proper account of the nonlinear geometric term due to the mid-plane stretching and of an applied axial load. The free nonlinear vibrations are studied with the energy balance method and the homotopy analysis method Liao (Commun Nonlinear Sci Numer Simul 14(4):983, 2009), thus carrying out a thorough analysis with regard to the nonlinear terms. The analysis is based on a single-degree-of-freedom model, where the nonlinear electric force acting on the beam is approximated by the Chebyshev method and a fringing field correction term is considered as well. A numerical solution, obtained by a 4th order Runge Kutta algorithm, is also proposed as a benchmark for all the semi-analytical results. Major attention is paid to verify the agreement between the different methods and the their accuracy in the pull-in regime.     

Scattering amplitudes from multivariate polynomial division

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.     

Automated one-loop calculations with GoSam

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the?loop.     

A prescribed scalar curvature-type equation: almost critical manifolds and multiple solutions

We present an asymptotic analysis for a perturbed prescribed scalar curvature-type equation. A major consequence is a non-existence result in low dimension. Conversely, we prove an existence result in higher dimensions: to this aim we develop a general finite-dimensional reduction procedure for perturbed variational functionals. The general principle can be useful to discuss some other nonlinear elliptic PDE with Sobolev critical growth in bounded domains.     

Improved formulation,branch-and-cut and tabu search heuristic for single loop material flow system design

The single loop material flow system design is a combinatorial optimization problem, arising in material handling system design, which amounts to designing an unidirectional loop flow pattern as well as to locate pickup and delivery stations. The objective is to minimize the time required to carry out all material flow movements between cells. In this paper, we develop valid inequalities for a previously proposed formulation. The valid inequalities are then embedded into a branch-and-cut framework which is shown to solve much larger instances to optimality than those reported in the literature. A tailored tabu search heuristic is also illustrated and computationally assessed.     

Existence results for forced nonlinear periodic BVPs at resonance

Sunto In questo lavoro si presentano alcuni risultati riguardanti l'esistenza di soluzioni p-periodiche per sistemi di equazioni differenziali non lineari in risonanza, del tipo x+ Dx + + Ag(t, x)=h(t), ove D ed A sono matrici m×m, con D di tipo diagonale, h è un termine forzante p-periodico e g è un campo vettoriale, non necessariamente limitato. In particolare, viene esteso ai sistemi, in ipotesi più generali, un classico teorema dovuto a Lazer e Leach. Le dimostrazioni sono basate sull'uso del grado topologico (teorema di continuazione di Mawhin).