Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

HD101584: Circumstellar characteristics and evolutionary status

We have performed a study of the characteristics of the circumstellar environment of the binary object HD101584, that provides information on a likely evolutionary scenario. We have obtained and analysed ALMA observations, complemented with observations using APEX, of a large number of molecular lines. An analysis of the spectral energy distribution has also been performed. Emissions from 12 molecular species (not counting isotopologues) have been observed, and most of them mapped with angular resolutions in the range 0.1" to 0.6". Four circumstellar components are identified: i) a central compact source of size 0.15", ii) an expanding equatorial density enhancement (a flattened density distribution in the plane of the orbit) of size 3", iii) a bipolar high-velocity outflow (150 km/s), and iv) an hourglass structure. The outflow is directed almost along the line of sight. There is evidence of a second bipolar outflow. The mass of the circumstellar gas is 0.5[D/1 kpc]^2 Msun, about half of it lies in the equatorial density enhancement. The dust mass is 0.01[D/1 kpc]^2 Msun, and a substantial fraction of this is in the form of large-sized, up to 1 mm, grains. The estimated kinetic age of the outflow is 770[D/1 kpc] yr. The kinetic energy and the scalar momentum of the accelerated gas are estimated to be 7x10^(45)[D/1 kpc]^2 erg and 10^(39)[D/1 kpc]^2 g cm/s, respectively. We provide good evidence that the binary system HD101584 is in a post-common-envelope-evolution phase, that ended before a stellar merger. Isotope ratios combined with stellar mass estimates suggest that the primary star's evolution was terminated already on the first red giant branch (RGB). Most of the energy required to drive the outflowing gas was probably released when material fell towards the companion.Comment: Accepted for publication in A&

Sweep, Step, Pulse, and Frequency-Based Techniques Applied to Protein Monolayer Electrochemistry at Nanoparticle Interfaces

Protein monolayer electrochemistry (PME), a strategy using synthetic platforms to study the electron transfer (ET) properties of adsorbed proteins, has been successfully applied to proteins adsorbed at monolayer-protected gold cluster (MPCs) assembled films, an adsorption interface shown to be an effective alternative, compared to traditional self-assembled monolayer (SAM) films, for the immobilization and study of ET proteins. Within PME studies, cyclic voltammetry (CV) remains the most commonly applied electrochemical technique in spite of several limitations that occur when the sweep technique is used at either platform. In particular, CV for PME at MPC films results in analysis complications stemming from the increased charging current inherent to electrochemical interfaces incorporating MPCs with capacitive properties. In this study, multiple electroanalytical techniques, involving step (chronocoulometry, CC), pulse (square wave voltammetry, SWV), and frequency-based impedance (electrochemical impedance spectroscopy, EIS) measurements, are applied to monolayers of adsorbed Pseudomonas aeruginosa azurin and horse heart cytochrome c at both MPC film assemblies as well as traditional SAMs. Electrochemical parameters (formal potential, electroactive surface coverage, double-layer capacitance, and ET rate constant) measured from these various techniques are directly compared and offer insight into the performance and reliability of each technique’s effectiveness in PME. While certain techniques result in measurements indistinguishable from CV, others offer distinct differences. Moreover, the application of alternative techniques reveals systemic limitations and complications within the electrochemical analysis that we further explore, including strategies for applying fast scanning techniques like SWV as well as the construction of MPC platforms with controlled levels of charging current that enable successful impedance analysis. The application of more advanced electrochemical techniques to developing electrochemical interfaces such as MPC film assemblies allows for a greater understanding of not only PME but also the applicability and effectiveness of these techniques to optimize the measurement of specific electrochemical parameters

Autocorrelation analysis for the unbiased determination of power-law exponents in single-quantum-dot blinking

We present an unbiased and robust analysis method for power-law blinking statistics in the photoluminescence of single nano-emitters, allowing us to extract both the bright- and dark-state power-law exponents from the emitters' intensity autocorrelation functions. As opposed to the widely-used threshold method, our technique therefore does not require discriminating the emission levels of bright and dark states in the experimental intensity timetraces. We rely on the simultaneous recording of 450 emission timetraces of single CdSe/CdS core/shell quantum dots at a frame rate of 250 Hz with single photon sensitivity. Under these conditions, our approach can determine ON and OFF power-law exponents with a precision of 3% from a comparison to numerical simulations, even for shot-noise-dominated emission signals with an average intensity below 1 photon per frame and per quantum dot. These capabilities pave the way for the unbiased, threshold-free determination of blinking power-law exponents at the micro-second timescale

Impact of irreversibility and uncertainty on the timing of infrastructure projects

This paper argues that because of the irreversibility and uncertainty associated with Build - Operate - Transfer (BOT) infrastructure projects, their financial evaluation should also routinely include the determination of the value of the option to defer the construction start-up. This ensures that project viability is comprehensively assessed before any revenue or loan guarantees are considered by project sponsors to support the project. This paper shows that the framework can be used even in the context of the intuitive binomial lattice model. This requires estimating volatility directly from the evolution of the net operating income while accounting for the correlation between the revenue and costs functions. This approach ensures that the uncertainties usually associated with toll revenues, in particular, are thoroughly investigated and their impact on project viability is thoroughly assessed. This paper illustrates the usefulness of the framework with data from an actual (BOT) toll road project. The results show that by postponing the project for a couple of years the project turns out to be viable, whereas it was not without the deferral. The evaluation approach proposed therefore provides a better framework for determining when and the extent of government financial support, if any, that may be needed to support a BOT project on the basis of project economics. The analysis may also be applicable to private sector investment projects, which are characterized by irreversibility and a high rate of uncertainty