A New Approach to Equations with Memory

We discuss a novel approach to the mathematical analysis of equations with memory, based on a new notion of state. This is the initial configuration of the system at time t = 0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function ${G : \mathbb{R}^+ \to \mathbb{R}^+}We discuss a novel approach to the mathematical analysis of equations with memory, based on a new notion of state. This is the initial configuration of the system at time t = 0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function G : \mathbbR⁺ ? \mathbbR⁺{G : \mathbb{R}^+ \to \mathbb{R}^+} such that

$G(0) = \lim_{s\to 0}G(s) > \lim_{s\to\infty}G(s) >0 $G(0) = \lim_{s\to 0}G(s) > \lim_{s\to\infty}G(s) >0      14. A free analogue of Hincin's characterization of infinite divisibility      Hari Bercovici  Vittorino Pata 《Proceedings of the American Mathematical Society》2000,128(4):1011-1015 Hincin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.       15. The Effect of Temperature and Magnetic Field on the Precipitation of Insoluble Salts of Alkaline Earth Metals      Raudino  Martina  Sarri  Filippo  Tatini  Duccio  Ambrosi  Moira  Aloisi  Giovanni Domenico  Ninham  Barry W.  Dei  Luigi  Lo Nostro  Pierandrea 《Journal of solution chemistry》2020,49(3):289-305 Journal of Solution Chemistry - A study of the effects induced by a weak magnetic field of about 0.4 T on the precipitation of insoluble alkaline earth carbonates is reported. Optical...      16. Membrane solubilization by detergent: resistance conferred by thickness      Pata V  Ahmed F  Discher DE  Dant N 《Langmuir : the ACS journal of surfaces and colloids》2004,20(10):3888-3893 The commonly held model for membrane dissolution by detergents/surfactants requires lipid transport from the inner to the outer bilayer leaflet ('flip-flop'). Although applicable to many systems, it fails in cases where cross-bilayer transport of membrane components is suppressed. In this paper we investigate the mechanism for surfactant-induced solubilization of polymeric bilayers. To that end, we examine the dissolution of a series of increasingly thick, polymer-based vesicles (polymersomes) by a nonionic surfactant, Triton X-100, using dynamic light scattering. We find that increasing the bilayer thickness imparts better resistance to dissolution, so that the concentration required for solubilization, after a fixed amount of time, increases nearly linearly with membrane thickness. Combining our experimental data with a theoretical model, we show that the dominant mechanism for the surfactant-induced dissolution of polymeric vesicles, where polymer flip-flop across the membrane is suppressed, is the surfactant transport through the bilayer. This mechanism is different both qualitatively and quantitatively from the mechanisms by which surfactants dissolve pure lipid vesicles.      17. Detection of honeybee venom in envenomed tissues by direct MALDI MSI      Francese S  Lambardi D  Mastrobuoni G  la Marca G  Moneti G  Turillazzi S 《Journal of the American Society for Mass Spectrometry》2009,20(1):112-123 A new analytical approach using matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) for the study of honeybee venom is shown. In vitro and in vivo models simulating the bee sting have been developed using live honeybees and, as the envenomation sites, pig ears and rat legs; MALDI MSI has been used to map, over time, the diffusion and distribution of three venom allergens (Api m 1, Api m 4, and Api m 6) and two venom toxins (apamine and mast cell degranulating peptide). In conjunction with other classical biochemical techniques and high resolution mass spectrometry (HRMS), structural data have been obtained that contribute to current understanding of honeybee venom composition. Initial data have also been obtained demonstrating the feasibility of mapping the organism's response to the sting. The opportunity to monitor venom diffusion and the organism's response at the same time might open new pathways for in vivo preclinical studies in designing and testing new venom immunotherapy (VIT).      18. Stability and exponential stability in linear viscoelasticity      Vittorino Pata 《Milan Journal of Mathematics》2009,77(1):333-360 In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ${\partial_{tt}}u(t) - \Delta u(t) + {\int_0^\infty} \mu(s) \Delta u(t - s) {\rm{d}}s = 0$ describing the dynamics of linearly viscoelastic bodies.      19. Superlinear Indefinite Equations on the Real Line and Chaotic Dynamics      Anna CapiettoWalter Dambrosio  Duccio Papini 《Journal of Differential Equations》2002,181(2):419-438       20. A construction of a robust family of exponential attractors      Stefania Gatti  Maurizio Grasselli  Alain Miranville  Vittorino Pata 《Proceedings of the American Mathematical Society》2006,134(1):117-127 Given a dissipative strongly continuous semigroup depending on some parameters, we construct a family of exponential attractors which is robust, in the sense of the symmetric Hausdorff distance, with respect to (even singular) perturbations.       [首页] « 上一页 [1] 2 [3] [4] [5] [6] [7] 下一页 » 末  页»

A free analogue of Hincin's characterization of infinite divisibility

Hincin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.

     

The Effect of Temperature and Magnetic Field on the Precipitation of Insoluble Salts of Alkaline Earth Metals

Journal of Solution Chemistry - A study of the effects induced by a weak magnetic field of about 0.4 T on the precipitation of insoluble alkaline earth carbonates is reported. Optical...     

Membrane solubilization by detergent: resistance conferred by thickness

The commonly held model for membrane dissolution by detergents/surfactants requires lipid transport from the inner to the outer bilayer leaflet ('flip-flop'). Although applicable to many systems, it fails in cases where cross-bilayer transport of membrane components is suppressed. In this paper we investigate the mechanism for surfactant-induced solubilization of polymeric bilayers. To that end, we examine the dissolution of a series of increasingly thick, polymer-based vesicles (polymersomes) by a nonionic surfactant, Triton X-100, using dynamic light scattering. We find that increasing the bilayer thickness imparts better resistance to dissolution, so that the concentration required for solubilization, after a fixed amount of time, increases nearly linearly with membrane thickness. Combining our experimental data with a theoretical model, we show that the dominant mechanism for the surfactant-induced dissolution of polymeric vesicles, where polymer flip-flop across the membrane is suppressed, is the surfactant transport through the bilayer. This mechanism is different both qualitatively and quantitatively from the mechanisms by which surfactants dissolve pure lipid vesicles.     

Detection of honeybee venom in envenomed tissues by direct MALDI MSI

A new analytical approach using matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) for the study of honeybee venom is shown. In vitro and in vivo models simulating the bee sting have been developed using live honeybees and, as the envenomation sites, pig ears and rat legs; MALDI MSI has been used to map, over time, the diffusion and distribution of three venom allergens (Api m 1, Api m 4, and Api m 6) and two venom toxins (apamine and mast cell degranulating peptide). In conjunction with other classical biochemical techniques and high resolution mass spectrometry (HRMS), structural data have been obtained that contribute to current understanding of honeybee venom composition. Initial data have also been obtained demonstrating the feasibility of mapping the organism's response to the sting. The opportunity to monitor venom diffusion and the organism's response at the same time might open new pathways for in vivo preclinical studies in designing and testing new venom immunotherapy (VIT).     

Stability and exponential stability in linear viscoelasticity

In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ${\partial_{tt}}u(t) - \Delta u(t) + {\int_0^\infty} \mu(s) \Delta u(t - s) {\rm{d}}s = 0$ describing the dynamics of linearly viscoelastic bodies.     

A construction of a robust family of exponential attractors

Given a dissipative strongly continuous semigroup depending on some parameters, we construct a family of exponential attractors which is robust, in the sense of the symmetric Hausdorff distance, with respect to (even singular) perturbations.