Watermark options

We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional problems as the unique solutions to highly non-linear first order ODEs that have the characteristics of a separatrix. The asymptotic growth of these free-boundary functions can take qualitatively different forms depending on parameter values, which is an interesting new feature

A Tale of Two Narrow-Line Regions: Ionization, Kinematics, and Spectral Energy Distributions for a Local Pair of Merging Obscured Active Galaxies

We explore the gas ionization and kinematics, as well as the optical--IR spectral energy distributions for UGC 11185, a nearby pair of merging galaxies hosting obscured active galactic nuclei (AGNs), also known as SDSS J181611.72+423941.6 and J181609.37+423923.0 (J1816NE and J1816SW, $z \approx 0.04$). Due to the wide separation between these interacting galaxies ($\sim 23$ kpc), observations of these objects provide a rare glimpse of the concurrent growth of supermassive black holes at an early merger stage. We use BPT line diagnostics to show that the full extent of the narrow line emission in both galaxies is photoionized by an AGN and confirm the existence of a 10-kpc-scale ionization cone in J1816NE, while in J1816SW the AGN narrow-line region is much more compact (1--2 kpc) and relatively undisturbed. Our observations also reveal the presence of ionized gas that nearly spans the entire distance between the galaxies which is likely in a merger-induced tidal stream. In addition, we carry out a spectral analysis of the X-ray emission using data from {\em XMM-Newton}. These galaxies represent a useful pair to explore how the [\ion{O}{3}] luminosity of an AGN is dependent on the size of the region used to explore the extended emission. Given the growing evidence for AGN "flickering" over short timescales, we speculate that the appearances and impact of these AGNs may change multiple times over the course of the galaxy merger, which is especially important given that these objects are likely the progenitors of the types of systems commonly classified as "dual AGNs."Comment: 15 pages, 10 figures, accepted by the Astrophysical Journa

Flatness-Based Control Approach to Drug Infusion for Cardiac Function Regulation

A new control method based on differential flatness theory is developed in this study, aiming at solving the problem of regulation of haemodynamic parameters. Actually control of the cardiac output (volume of blood pumped out by heart per unit of time) and of the arterial blood pressure is achieved through the administered infusion of cardiovascular drugs such as dopamine and sodium nitroprusside. Time delays between the control inputs and the system's outputs are taken into account. Using the principle of dynamic extension, which means that by considering certain control inputs and their derivatives as additional state variables, a state-space description for the heart's function is obtained. It is proven that the dynamic model of the heart is a differentially flat one. This enables its transformation into a linear canonical and decoupled form, for which the design of a stabilising feedback controller becomes possible. The proposed feedback controller is of proven stability and assures fast and accurate tracking of the reference setpoints by the outputs of the heart's dynamic model. Moreover, by using a Kalman filter-based disturbances' estimator, it becomes possible to estimate in real-time and compensate for the model uncertainty and external perturbation inputs that affect the heart's model. © The Institution of Engineering and Technology

Discretionary stopping of stochastic differential equations with generalised drift

We consider the problem of optimally stopping a general one-dimensional stochastic differential equation (SDE) with generalised drift over an infinite time horizon. First, we derive a complete characterisation of the solution to this problem in terms of vari- ational inequalities. In particular, we prove that the problem’s value function is the difference of two convex functions and satisfies an appropriate variational inequality in the sense of distributions. We also establish a verification theorem that is the strongest one possible because it involves only the optimal stopping problem’s data. Next, we derive the complete explicit solution to the problem that arises when the state process is a skew geometric Brownian motion and the reward function is the one of a financial call option. In this case, we show that the optimal stopping strategy can take sev- eral qualitatively different forms, depending on parameter values. Furthermore, the explicit solution to this special case shows that the so-called “principle of smooth fit” does not hold in general for optimal stopping problems involving solutions to SDEs with generalised drift

A Tale of Two Narrow-Line Regions: Ionization, Kinematics, and Spectral Energy Distributions for a Local Pair of Merging Obscured Active Galaxies

We explore the gas ionization and kinematics, as well as the optical-IR spectral energy distributions for UGC 11185, a nearby pair of merging galaxies hosting obscured active galactic nuclei (AGNs), also known as SDSS J181611.72+423941.6 and J181609.37+423923.0 (J1816NE and J1816SW, z ≈ 0.04). Due to the wide separation between these interacting galaxies (~23 kpc), observations of these objects provide a rare glimpse of the concurrent growth of supermassive black holes at an early merger stage. We use BPT line diagnostics to show that the full extent of the narrow-line emission in both galaxies is photoionized by an AGN, and confirm the existence of a 10 kpc-scale ionization cone in J1816NE, while in J1816SW the AGN narrow-line region is much more compact (1–2 kpc) and relatively undisturbed. Our observations also reveal the presence of ionized gas that nearly spans the entire distance between the galaxies, which is likely in a merger-induced tidal stream. In addition, we carry out a spectral analysis of the X-ray emission using data from XMM-Newton. These galaxies represent a useful pair to explore how the [O iii] luminosity of an AGN is dependent on the size of the region used to explore the extended emission. Given the growing evidence for AGN flickering over short timescales, we speculate that the appearances and impacts of these AGNs may change multiple times over the course of the galaxy merger, which is especially important given that these objects are likely the progenitors of the types of systems commonly classified as dual AGNs

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.Comment: 36 page

Synthesis of Tin Nitride SnxNyNanowires by Chemical Vapour Deposition

Tin nitride (SnxNy) nanowires have been grown for the first time by chemical vapour deposition on n-type Si(111) and in particular by nitridation of Sn containing NH4Cl at 450 °C under a steady flow of NH3. The SnxNynanowires have an average diameter of 200 nm and lengths ≥5 μm and were grown on Si(111) coated with a few nm’s of Au. Nitridation of Sn alone, under a flow of NH3is not effective and leads to the deposition of Sn droplets on the Au/Si(111) surface which impedes one-dimensional growth over a wide temperature range i.e. 300–800 °C. This was overcome by the addition of ammonium chloride (NH4Cl) which undergoes sublimation at 338 °C thereby releasing NH3and HCl which act as dispersants thereby enhancing the vapour pressure of Sn and the one-dimensional growth of SnxNynanowires. In addition to the action of dispersion, Sn reacts with HCl giving SnCl2which in turn reacts with NH3leading to the formation of SnxNyNWs. A first estimate of the band-gap of the SnxNynanowires grown on Si(111) was obtained from optical reflection measurements and found to be ≈2.6 eV. Finally, intricate assemblies of nanowires were also obtained at lower growth temperatures

Liax Is a Surrogate Marker For Cell Envelope Stress and Daptomycin Non-Susceptibility in Enterococcus Faecium

Daptomycin (DAP) is often used as a first-line therapy to treat vancomycin-resistan