Differential-algebraic jet spaces preserve internality to the constants

This paper concerns the model theory of jet spaces (i.e., higher-order tangent spaces) in differentially closed fields. Suppose p is the generic type of the jet space to a finite dimensional differential-algebraic variety at a generic point. It is shown that p satisfies a certain strengthening of almost internality to the constant field called "preserving internality to the constants". This strengthening is a model-theoretic abstraction of the generic behaviour of jet spaces in complex-analytic geometry. A counterexample is constructed showing that only this generic analogue holds in differential-algebraic geometry.Comment: 13 page

In Vitro Evaluation of Loaded Chitosan Membranes for Pain Relief and Infection Prevention

Wounds resulting from musculoskeletal trauma cause pain and often infection of damaged tissue. Up to 80% of these infections are due to biofilm formation on wounded tissue. Bacteria within a biofilm can withstand 1000X the minimum inhibitory concentration of antibiotics, demonstrating the need for new therapeutics to prevent and treat these infections. Cis-2-decenoic acid (C2DA) disperses biofilms and can prevent biofilm formation of many microorganisms. Additionally, local anesthetics like bupivacaine have antimicrobial effects against bacteria. This study sought to evaluate modified electrospun chitosan membranes as wound dressings that release C2DA and bupivacaine to prevent infection and alleviate pain associated with wounds. Release profiles of therapeutics were evaluated, with results indicating that membranes release active concentrations of both therapeutics for 72 hours. Though higher concentrations of bupivacaine were not cytocompatible with fibroblasts, membranes were effective in preventing Methicillin-resistant Staphylococcus aureus biofilm growth in vitro

A computational triage approach to the synthesis of novel difluorocyclopentenes and fluorinated cycloheptadienes using thermal rearrangements

Electronic structure calculations have been used for the effective triage of substituent effects on difluorinated vinylcyclopropane precursors and their ability to undergo vinyl cyclopropane rearrangements (VCPR). Groups which effectively stabilised radicals, specifically heteroarenes, were found to result in the lowest energy barriers. Ten novel precursors were synthesised to test the accuracy of computational predictions; the most reactive species which contained heteroarenes underwent thermal rearrangements at room temperature to afford novel difluorocyclopentenes and fluorinated benzocycloheptadienes through competing VCPR and [3,3]-rearrangement pathways, respectively. More controlled rearrangement of ethyl 3-(1’(2’2’-difluoro-3’benzo[d][1,3]dioxol-5-yl)cyclopropyl) propenoate (22) allowed these competing pathways to be monitored at the same time and activation energies for both reactions were determined; Ea(VCPR) = (23.4 ± 0.2) kcal mol-1 and Ea([3,3]) = (24.9 ± 0.3) kcal mol-1. Comparing our calculated activation energies with these parameters showed that no single method stood out as the most accurate for predicting barrier heights; (U)M05-2X/6-31+G* methodology remained the best for VCPR but M06-2X/6-31G* was better for the [3,3]-rearrangement. The consistency observed with (U)B3LYP/6-31G* calculations meant that it came closest to a universal method for dealing with these systems. The developed computational design model correctly predicted the observed selectivity of rearrangement pathways for both our system and literature compounds

P2_6 Surfin' Fury

In a short film called Kung Fury, the main hero uses a person as a surfing board. We investigated the force he would need to push himself forward based on the kinetic friction and drag force. The force ranges between -335.24 ± 6.87 N and -980.74 ± 6.87 N

P2_4 Not So Spontaneous Combustion

In the X-Files TV series, a man is injected with a chemical that freezes him. When defrosting, his bodystarts producing exothermic reaction that sets him on re. At normal metabolic rate, this reaction wouldtake at least 4 days 15 hours and 24 minutes. In the time scale of the show the energy required to heatthe body would be 9.9 x 105 W

P2_1 In a Blink of an Eye

The game World of Warcraft allows a mage to teleport a short distance in almost an instant. Based on the description of the spell, we calculated the acceleration of the mage as 82.86 ± 13.96g. We then compared the acceleration of the mage to those that people are able to survive in real life

P2_5 Jovian Gravitational Perturbations on Earth's Orbit

In a hypothetical situations in which the solar system contains varied masses of Jupiter, the orbit of the Earth may fall subject to considerable gravitational perturbations. With the aid of the Newtonian gravity simulator, Universe SandboxTM, the effects of these perturbations can be observed .The orbit is found alter by an approximate 30x106 km before being ejected from the solar system, at Jovian mass of 0.7 Mʘ