On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

$$\left( {\mathop \Sigma \limits_{i = 1}^\infty \mathop \Sigma \limits_{j = 1}^\infty a_{ij}^{(n)} \mu ^i *v^j ,n \in \mathbb{N}} \right)$$     

Electrochemical behaviour of V2O5 xerogel in aqueous LiNO3 solution

By dissolving crystalline V₂O₅ in hydrogen peroxide and drying at elevated temperature, the V₂O₅ xerogel was obtained. Its electrochemical behaviour was examined in aqueous solution of LiNO₃ by both cyclic voltammetry and galvanostatic charging/discharging cycling. Peak-to-peak potential separation observed at the cyclovoltammograms indicated fast Li⁺ intercalation/deintercalation reactions. Initial discharge capacity amounted to 69 mAhg^?1, and after 100 charging/discharging cycles, capacity fade amounted to 11% only. This presents a remarkable improvement in comparison with the behaviour of crystalline, vanadium oxide based, lithium intercalates in aqueous electrolytes.     

The improvement of the Li-ion insertion behaviour of Li1.05Cr0.10Mn1.85O4 in an aqueous medium upon addition of vinylene carbonate

The influence of vinylene carbonate addition to aqueous LiNO₃ solution on the Li-ion insertion performance of a Li_1.05Cr_0.10Mn_1.85O₄ was studied by galvanostatic charging/discharging. Without additive, the coulombic capacity amounted initially to 80 mA h g^?1 and, during 50 galvanostatic charging/discharging cycles, decreased to 44.1% of the initial value. Upon VC addition in an amount of 1 wt.%, the initial discharge capacity of 112 mA h g^?1 was registered which after 100th charging/discharging cycles retained even 82% of the initial value. This is the first report of a successful use of an additive to improve the behaviour of a Li-intercalation material in an aqueous solution.     

Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction–diffusion equations

We consider front propagation in a family of scalar reaction–diffusion equations in the asymptotic limit where the polynomial degree of the potential function tends to infinity. We investigate the Gevrey properties of the corresponding critical propagation speed, proving that the formal series expansion for that speed is Gevrey-1 with respect to the inverse of the degree. Moreover, we discuss the question of optimal truncation. Finally, we present a reliable numerical algorithm for evaluating the coefficients in the expansion with arbitrary precision and to any desired order, and we illustrate that algorithm by calculating explicitly the first ten coefficients. Our analysis builds on results obtained previously in [F. Dumortier, N. Popovi?, T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction–diffusion equations, J. Math. Anal. Appl. 326 (2) (2007) 1007–1023], and makes use of the blow-up technique in combination with geometric singular perturbation theory and complex analysis, while the numerical evaluation of the coefficients in the expansion for the critical speed is based on rigorous interval arithmetic.     

Photophysics of the fluorescent pH indicator BCECF

The photophysical behavior of BCECF [2',7'-bis-(2-carboxyethyl)-5-(and-6)-carboxyfluorescein]--currently the most widely used fluorescent pH indicator for near-neutral intracellular pH measurements--has been explored by using absorption and steady-state and time-resolved fluorescence measurements. The influence of ionic strength as well as total buffer concentration on the absorbance and steady-state fluorescence has been investigated. The apparent acidity constant of the pH indicator determined by absorbance and fluorescence titration is dependent on the added buffer and salt concentrations. A semiempirical model is proposed to rationalize the variations in the apparent pKa values. The excited-state proton exchange of BCECF at physiological pH becomes reversible upon addition of phosphate buffer, inducing a pH-dependent change of the fluorescence decay times. Fluorescence decay traces collected as a function of total buffer concentration and pH were analyzed by global compartmental analysis yielding the following values of the rate constants describing excited-state dynamics of BCECF: k01 = 3.4 x 10(8) s(-1), k02 = 2.6 x 10(8) s(-1), k21 approximately 1 x 10(6) M(-1) s(-1), k12(B) = 1.4 x 10(8) M(-1) s(-1), and k21(B) = 4.3 x 10(7) M(-1) s(-1).     

Probability in Theories With Complex Dynamics and Hardy’s Fifth Axiom

L. Hardy has formulated an axiomatization program of quantum mechanics and generalized probability theories that has been quite influential. In this paper, properties of typical Hamiltonian dynamical systems are used to argue that there are applications of probability in physical theories of systems with dynamical complexity that require continuous spaces of pure states. Hardy’s axiomatization program does not deal with such theories. In particular Hardy’s fifth axiom does not differentiate between such applications of classical probability and quantum probability.     

A geometric approach to bistable front propagation in scalar reaction–diffusion equations with cut-off

‘Cut-offs’ were introduced to model front propagation in reaction–diffusion systems in which the reaction is effectively deactivated at points where the concentration lies below some threshold. In this article, we investigate the effects of a cut-off on fronts propagating into metastable states in a class of bistable scalar equations. We apply the method of geometric desingularization from dynamical systems theory to calculate explicitly the change in front propagation speed that is induced by the cut-off. We prove that the asymptotics of this correction scales with fractional powers of the cut-off parameter, and we identify the source of these exponents, thus explaining the structure of the resulting expansion. In particular, we show geometrically that the speed of bistable fronts increases in the presence of a cut-off, in agreement with results obtained previously via a variational principle. We first discuss the classical Nagumo equation as a prototypical example of bistable front propagation. Then, we present corresponding results for the (equivalent) cut-off Schlögl equation. Finally, we extend our analysis to a general family of reaction–diffusion equations that support bistable fronts, and we show that knowledge of an explicit front solution to the associated problem without cut-off is necessary for the correction induced by the cut-off to be computable in closed form.