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&

Biomechanical Tolerance of Whole Lumbar Spines in Straightened Posture Subjected to Axial Acceleration

Quantification of biomechanical tolerance is necessary for injury prediction and protection of vehicular occupants. This study experimentally quantified lumbar spine axial tolerance during accelerative environments simulating a variety of military and civilian scenarios. Intact human lumbar spines (T12‐L5) were dynamically loaded using a custom‐built drop tower. Twenty‐three specimens were tested at sub‐failure and failure levels consisting of peak axial forces between 2.6 and 7.9 kN and corresponding peak accelerations between 7 and 57 g. Military aircraft ejection and helicopter crashes fall within these high axial acceleration ranges. Testing was stopped following injury detection. Both peak force and acceleration were significant (p \u3c 0.0001) injury predictors. Injury probability curves using parametric survival analysis were created for peak acceleration and peak force. Fifty‐percent probability of injury (95%CI) for force and acceleration were 4.5 (3.9–5.2 kN), and 16 (13–19 g). A majority of injuries affected the L1 spinal level. Peak axial forces and accelerations were greater for specimens that sustained multiple injuries or injuries at L2–L5 spinal levels. In general, force‐based tolerance was consistent with previous shorter‐segment lumbar spine testing (3–5 vertebrae), although studies incorporating isolated vertebral bodies reported higher tolerance attributable to a different injury mechanism involving structural failure of the cortical shell. This study identified novel outcomes with regard to injury patterns, wherein more violent exposures produced more injuries in the caudal lumbar spine. This caudal migration was likely attributable to increased injury tolerance at lower lumbar spinal levels and a faster inertial mass recruitment process for high rate load application. Published 2017. This article is a U.S. Government work and is in the public domain in the USA

The Critical Role of Water at the Gold-titania Interface in Catalytic CO Oxidation

We provide direct evidence of a water-mediated reaction mechanism for room-temperature CO oxidation over Au/TiO2 catalysts. A hydrogen/deuterium kinetic isotope effect of nearly 2 implicates O-H(D) bond breaking in the rate-determining step. Kinetics and in situ infrared spectroscopy experiments showed that the coverage of weakly adsorbed water on TiO2 largely determines catalyst activity by changing the number of active sites. Density functional theory calculations indicated that proton transfer at the metal-support interface facilitates O2 binding and activation; the resulting Au-OOH species readily reacts with adsorbed Au-CO, yielding Au-COOH. Au-COOH decomposition involves proton transfer to water and was suggested to be rate determining. These results provide a unified explanation to disparate literature results, clearly defining the mechanistic roles of water, support OH groups, and the metal-support interface

NaBr Poisoning of Au/TiO\u3csub\u3e2\u3c/sub\u3e Catalysts: Effects on Kinetics, Poisoning Mechanism, and Estimation of the Number of Catalytic Active Sites

Sodium bromide was used to intentionally poison a commercial Au/TiO2 catalyst with the goals of understanding the nature of halide poisoning and evaluating the number and nature of the catalytic active sites. A series of eight poisoned catalysts were prepared by impregnating the parent catalyst with methanolic solutions of NaBr. Each catalyst was tested with CO oxidation catalysis under differential reactor conditions; O2 reaction orders and Arrhenius activation energies were determined for each material. All of the kinetic data, including a Michaelis−Menten analysis, indicated that the primary effect of adding NaBr was to reduce the number of catalytically active sites. Density functional theory calculations, employed to evaluate likely binding sites for NaBr, showed that NaBr binds more strongly to Au corner and edge atoms than it does to the titania support or to exposed Au face atoms. Infrared spectroscopy of adsorbed CO, along with a Temkin analysis of the data, was also used to evaluate changes to the catalyst upon NaBr deposition. These studies suggested that NaBr addition induces some subtle changes in the coverage dependent properties of CO adsorption, but that these did not substantially impact the CO coverage of the CO binding sites. The experimental and computational results are discussed in terms of possible poisoning mechanisms (siteblocking vs off-site binding and modification); the nature and number of active sites are also discussed in the context of the results

Cost-Effectiveness of Primary versus Secondary Prophylaxis with Pegfilgrastim in Women with Early-Stage Breast Cancer Receiving Chemotherapy

AbstractObjectiveProphylaxis with granulocyte colony-stimulating factor (G-CSF) reduces the risk of febrile neutropenia (FN) in patients receiving myelosuppressive chemotherapy. We estimated the incremental cost-effectiveness of G-CSF pegfilgrastim primary (starting in cycle 1 and continuing in subsequent cycles of chemotherapy) versus secondary (only after an FN event) prophylaxis in women with early-stage breast cancer receiving myelosuppressive chemotherapy with a ≥20% FN risk.MethodsA decision-analytic model was constructed from a health insurer's perspective with a lifetime study horizon. The model considers direct medical costs and outcomes related to reduced FN and potential survival benefits because of reduced FN-related mortality. Inputs for the model were obtained from the medical literature. Sensitivity analyses were conducted across plausible ranges in parameter values.ResultsThe incremental cost-effectiveness ratio (ICER) of pegfilgrastim as primary versus secondary prophylaxis was $48,000/FN episode avoided. Adding survival benefit from avoiding FN mortality yielded an ICER of$110,000/life-year gained (LYG) or $116,000/quality-adjusted life-year (QALY) gained. The most influential factors included FN case-fatality, FN relative risk reduction from primary prophylaxis, and age at diagnosis.ConclusionsCompared with secondary prophylaxis, the cost-effectiveness of pegfilgrastim as primary prophylaxis may be equivalent or superior to other commonly used supportive care interventions for women with breast cancer. Further assessment of the direct impact of G-CSF on short- and long-term survival is needed to substantiate these findings

LNK (SH2B3): paradoxical effects in ovarian cancer.

LNK (SH2B3) is an adaptor protein studied extensively in normal and malignant hematopoietic cells. In these cells, it downregulates activated tyrosine kinases at the cell surface resulting in an antiproliferative effect. To date, no studies have examined activities of LNK in solid tumors. In this study, we found by in silico analysis and staining tissue arrays that the levels of LNK expression were elevated in high-grade ovarian cancer. To test the functional importance of this observation, LNK was either overexpressed or silenced in several ovarian cancer cell lines. Remarkably, overexpression of LNK rendered the cells resistant to death induced by either serum starvation or nutrient deprivation, and generated larger tumors using a murine xenograft model. In contrast, silencing of LNK decreased ovarian cancer cell growth in vitro and in vivo. Western blot studies indicated that overexpression of LNK upregulated and extended the transduction of the mitogenic signal, whereas silencing of LNK produced the opposite effects. Furthermore, forced expression of LNK reduced cell size, inhibited cell migration and markedly enhanced cell adhesion. Liquid chromatography-mass spectroscopy identified 14-3-3 as one of the LNK-binding partners. Our results suggest that in contrast to the findings in hematologic malignancies, the adaptor protein LNK acts as a positive signal transduction modulator in ovarian cancers