An interval branch and bound method for global Robust optimization

In this paper, we design a Branch and Bound algorithm based on interval arithmetic to address nonconvex robust optimization problems. This algorithm provides the exact global solution of such difficult problems arising in many real life applications. A code was developed in MatLab and was used to solve some robust nonconvex problems with few variables. This first numerical study shows the interest of this approach providing the global solution of such difficult robust nonconvex optimization problems.

     

k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

Analysis Mathematica - We introduce and study the k-Hankel Gabor transform. We investigate the localization operators for this transform. In particular, we study their trace class properties and we...     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Diffusion of Gold Nanoparticles in Inverse Opals Probed by Heterodyne Dynamic Light Scattering

The diffusive behavior of nanoparticles inside porous materials is attracting a lot of interest in the context of understanding, modeling, and optimization of many technical processes. A very powerful technique for characterizing the diffusive behavior of particles in free media is dynamic light scattering (DLS). The applicability of the method in porous media is considered, however, to be rather difficult due to the presence of multiple sources of scattering. In contrast to most of the previous approaches, the DLS method was applied without ensuring matching refractive indices of solvent and porous matrix in the present study. To test the capabilities of the method, the diffusion of spherical gold nanoparticles within the interconnected, periodic nanopores of inverse opals was analyzed. Despite the complexity of this system, which involves many interfaces and different refractive indices, a clear signal related to the motion of particles inside the porous media was obtained. As expected, the diffusive process inside the porous sample slowed down compared to the particle diffusion in free media. The obtained effective diffusion coefficients were found to be wave vector-dependent. They increased linearly with increasing spatial extension of the probed particle concentration fluctuations. On average, the slowing-down factor measured in this work agrees within combined uncertainties with literature data.

     

Naphthalimide‐phthalimide derivative based photoinitiating systems for polymerization reactions under blue lights

Naphthalimide‐phthalimide derivatives (NDPDs) have been synthesized and combined with an iodonium salt, N‐vinylcarbazole, amine or 2,4,6‐tris(trichloromethyl)‐1,3,5‐triazine to produce reactive species (i.e., radicals and cations). These generated reactive species are capable of initiating the cationic polymerization of epoxides and/or the radical polymerization of acrylates upon exposure to very soft polychromatic visible lights or blue lights. Compared with the well‐known camphorquinone based systems used as references, the novel NDPD based combinations employed here demonstrate clearly higher efficiencies for the cationic polymerization of epoxides under air as well as the radical polymerization of acrylates. Remarkably, one of the NDPDs (i.e., NDPD2) based systems is characterized by an outstanding reactivity. The structure/reactivity/efficiency relationships of the investigated NDPDs were studied by fluorescence, cyclic voltammetry, laser flash photolysis, electron spin resonance spin trapping, and steady state photolysis techniques. The key parameters for their reactivity are provided. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 665–674