Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

A unified treatment of dividend payment problems under fixed cost and implementation delays

In this paper we study the dividend optimization problem for a corporation or a financial institution when the management faces (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein–Uhlenbeck and square-root processes. Since the cash flow structure of different companies have different qualitative behaviors, it makes sense to use different diffusions to model them. The delay causes significant difficulties to the optimization problem since the cash reservoir fluctuates during the delay period. We provide a uniform mathematical framework to analyze all the models and provide optimal threshold strategies at which the management initiates actions, i.e., declaration and payment of dividends. Our solution depends on a new characterization of the value function for one-dimensional diffusions and provide easily implementable algorithms to find the optimal control and the value function.     

A Nanotubular Metal–Organic Framework with a Narrow Bandgap from Extended Conjugation**

A one-dimensional nanotubular metal–organic framework (MOF) [Ni(Cu-H₄TPPA)]⋅2 (CH₃)₂NH₂⁺ (H₈TPPA=5,10,15,20-tetrakis[p-phenylphosphonic acid] porphyrin) constructed by using the arylphosphonic acid H₈TPPA is reported. The structure of this MOF, known as GTUB-4 , was solved by using single-crystal X-ray diffraction and its geometric accessible surface area was calculated to be 1102 m² g⁻¹, making it the phosphonate MOF with the highest reported surface area. Due to the extended conjugation of its porphyrin core, GTUB-4 possesses narrow indirect and direct bandgaps (1.9 eV and 2.16 eV, respectively) in the semiconductor regime. Thermogravimetric analysis suggests that GTUB-4 is thermally stable up to 400 °C. Owing to its high surface area, low bandgap, and high thermal stability, GTUB-4 could find applications as electrodes in supercapacitors.     

Sequential tracking of a hidden Markov chain using point process observations

We study finite horizon optimal switching problems for hidden Markov chain models with point process observations. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state variable using Bayesian updates over the discrete observations. Such a model has applications in economic policy making, staffing under variable demand levels and generalized Poisson disorder problems. We show regularity of the value function and explicitly characterize an optimal strategy. We also provide an efficient numerical scheme and illustrate our results with several computational examples.     

Ultrasensitive measurements of microbial rhodopsin photocycles using photochromic FRET

Microbial rhodopsins are an important class of light-activated transmembrane proteins whose function is typically studied on bulk samples. Herein, we apply photochromic fluorescence resonance energy transfer to investigate the dynamics of these proteins with sensitivity approaching the single-molecule limit. The brightness of a covalently linked organic fluorophore is modulated by changes in the absorption spectrum of the endogenous retinal chromophore that occur as the molecule undergoes a light-activated photocycle. We studied the photocycles of blue-absorbing proteorhodopsin and sensory rhodopsin II (SRII). Clusters of 2-3 molecules of SRII clearly showed a light-induced photocycle. Single molecules of SRII showed a photocycle upon signal averaging over several illumination cycles.     

Multi-Scale Time-Changed Birth Processes for Pricing Multi-Name Credit Derivatives

Abstract

We develop two parsimonious models for pricing multi-name credit derivatives. We derive closed form expression for the loss distribution, which then can be used in determining the prices of tranche and index swaps and more exotic derivatives on these contracts. Our starting point is the model of Ding et al., 2008, which takes the loss process as a time-changed birth process. We introduce stochastic parameter variations into the intensity of the loss process and use the multi-time scale approach of Fouque et al., 2003 Fouque, J.-P., Papanicolaou, G., Sircar, R. and Solna, K. 2003. Multiscale stochastic volatility asymptotics. SIAM Journal of Multiscale Modeling and Simulation, 2(1): 22–42.  [Google Scholar] and obtain explicit perturbation approximations to the loss distribution. We demonstrate the competence of our approach by calibrating it to the CDX index data.     

Temperature-programmed oxidation of equilibrium fluid catalytic cracking catalysts

Characterization of coke on equilibrium, fluid catalytic cracking (FCC) catalysts contaminated with metals was investigated using temperature-programmed oxidation (TPO). TPO spectra of spent equilibrium catalysts from cracking of sour imported heavy gas oil (SIHGO) were deconvoluted into four peaks (Peak K, L, M and N). The four peaks were assigned to different types of coke on the catalyst. Peak L in the TPO spectrum was assigned to the 'contaminant' coke in the vicinity of metals. The amount of contaminant coke (Peak L) correlates with metal-contaminant concentration. The size of Peak L which is related to amount of contaminant coke decreased significantly for the spent highly contaminated catalyst pretreated with hydrogen and methane prior to cracking reactions as compared to the non-pretreated catalysts. Since both hydrogen and methane pretreatment can reduce oxidation state of the vanadium that present at high concentrations on the equilibrium catalysts the decrease in the amount of contaminant-coke represented by Peak L was explained by the reduction of the oxidation state of vanadium. Less contaminant coke was produced after the equilibrium catalysts were pretreated using hydrogen and methane gases since reduced vanadium has lower dehydrogenation activity compared to oxidized vanadium. This revised version was published online in August 2006 with corrections to the Cover Date.     

Characterization and recovery of tartaric acid from wastes of wine and grape juice industries

Tartaric acid is mainly used in food, pharmaceuticals and cosmetics industries. In this study, the waste samples, which contain tartaric acid, from the wastes of wine and grape juice industries were characterized by using TG, DSC, FTIR and XRD techniques. HPLC was used to determine tartaric acid content of samples. The decomposition temperatures of waste samples were found to be relatively higher compared with that of pure tartaric acid. This difference in decomposition temperatures was attributed to the presence of potassium tartrate since high potassium content was detected with ICP-AES.     

Optimal investment to minimize the probability of drawdown

We determine the optimal investment strategy in a Black–Scholes financial market to minimize the so-called probability of drawdown, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is subject to a payout that is a deterministic function of its value, as might be the case for an endowment fund paying at a specified rate, for example, at a constant rate or at a rate that is proportional to the fund’s value.