Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

Phosphoryl‐Rich Flame‐Retardant Ions (FRIONs): Towards Safer Lithium‐Ion Batteries

The functionalized catecholate, tetraethyl (2,3‐dihydroxy‐1,4‐phenylene)bis(phosphonate) (H₂‐DPC), has been used to prepare a series of lithium salts Li[B(DPC)(oxalato)], Li[B(DPC)₂], Li[B(DPC)F₂], and Li[P(DPC)₃]. The phosphoryl‐rich character of these anions was designed to impart flame‐retardant properties for their use as potential flame‐retardant ions (FRIONs), additives, or replacements for other lithium salts for safer lithium‐ion batteries. The new materials were fully characterized, and the single‐crystal structures of Li[B(DPC)(oxalato)] and Li[P(DPC)₃] have been determined. Thermogravimetric analysis of the four lithium salts show that they are thermally stable up to around 200 °C. Pyrolysis combustion flow calorimetry reveals that these salts produce high char yields upon combustion.     

Ranking Oxidant Sensitiveness: A Guide for Synthetic Utility

Common oxidants used in chemical synthesis, including newly developed perruthenates, were evaluated in the context of understanding (and better appreciating) the sensitiveness and associated potential hazards of these reagents. Analysis using sealed cell differential scanning calorimetry (scDSC) facilitated Yoshida correlations, which were compared to impact sensitiveness and electrostatic discharge experiments (ESD), that enabled sensitiveness ranking. Methyltriphenylphoshonium perruthenate (MTP3, 8 ), isoamyltriphenylphosphonium perruthenate (ATP3, 7 ) and tetraphenylphosphonium perruthenate (TP3, 9 ) were found to be the most sensitive followed by 2-iodoxybenzoic acid (IBX, 2 ) and benzoyl peroxide (BPO, 10 ), whereas the most benign were observed to be Oxone ( 12 ), manganese dioxide (MnO₂, 13 ), and N-bromosuccinimide (NBS, 17 ).     

Structure of Shocks in Burgers Turbulence with Lévy Noise Initial Data

We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by Lévy noise, or equivalently when the initial potential is a two-sided Lévy process ψ ₀. When ψ ₀ is abrupt in the sense of Vigon or has bounded variation with lim?sup_|h|↓0 h ^?2 ψ ₀(h)=∞, we prove that the set of points with zero velocity is regenerative, and that in the latter case this set is equal to the set of Lagrangian regular points, which is non-empty. When ψ ₀ is abrupt we show that the shock structure is discrete. When ψ ₀ is eroded we show that there are no rarefaction intervals.     

Bigger data,collaborative tools and the future of predictive drug discovery

Over the past decade we have seen a growth in the provision of chemistry data and cheminformatics tools as either free websites or software as a service commercial offerings. These have transformed how we find molecule-related data and use such tools in our research. There have also been efforts to improve collaboration between researchers either openly or through secure transactions using commercial tools. A major challenge in the future will be how such databases and software approaches handle larger amounts of data as it accumulates from high throughput screening and enables the user to draw insights, enable predictions and move projects forward. We now discuss how information from some drug discovery datasets can be made more accessible and how privacy of data should not overwhelm the desire to share it at an appropriate time with collaborators. We also discuss additional software tools that could be made available and provide our thoughts on the future of predictive drug discovery in this age of big data. We use some examples from our own research on neglected diseases, collaborations, mobile apps and algorithm development to illustrate these ideas.     

The complete family of Arnoux–Yoccoz surfaces

The family of translation surfaces (X _g , ω _g ) constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus g greater than or equal to 3. We triangulate these surfaces and deduce general properties they share. The surfaces (X _g , ω _g ) converge to a surface (X _∞, ω _∞) of infinite genus and finite area. We study the exchange on infinitely many intervals that arises from the vertical flow on (X _∞, ω _∞) and compute the affine group of (X _∞, ω _∞), which has an index 2 cyclic subgroup generated by a hyperbolic element.