Distinguishing between small Arkani-Hamed-Dimopoulos-Dvali and Randall-Sundrum accelerator-generated black holes

In models with extra dimensions that accommodate a TeV-scale gravity, small black holes could be produced in near future accelerator experiments. Such small black holes, whose gravitational radius is much smaller than the characteristic size of extra dimensions can be very well described by asymptotically flat solutions, thus losing the information about the global geometry of the extra manifold. One might conclude that such small black holes would be indistinguishable in different scenarios. We argue that important differences still exist, especially regarding experimental signature in colliders, which may help us distinguish between the various extra dimensional scenarios. The main differences come from the fact that most of the models with the warped extra dimension have an additional discrete Z2 symmetry that makes the brane behave as if it were an infinite tension brane.     

On a Problem of Cameron’s on Inexhaustible Graphs

A graph G is inexhaustible if whenever a vertex of G is deleted the remaining graph is isomorphic to G. We address a question of Cameron [6], who asked which countable graphs are inexhaustible. In particular, we prove that there are continuum many countable inexhaustible graphs with properties in common with the infinite random graph, including adjacency properties and universality. Locally finite inexhaustible graphs and forests are investigated, as is a semigroup structure on the class of inexhaustible graphs. We extend a result of [7] on homogeneous inexhaustible graphs to pseudo-homogeneous inexhaustible graphs.The authors gratefully acknowledge support from the Natural Science and Engineering Research Council of Canada (NSERC).     

Antibacterial effects of the essential oils of commonly consumed medicinal herbs using an in vitro model

The chemical composition and antibacterial activity of essential oils from 10 commonly consumed herbs: Citrus aurantium, C. limon, Lavandula angustifolia, Matricaria chamomilla, Mentha piperita, M. spicata, Ocimum basilicum, Origanum vulgare, Thymus vulgaris and Salvia officinalis have been determined. The antibacterial activity of these oils and their main components; i.e. camphor, carvacrol, 1,8-cineole, linalool, linalyl acetate, limonene, menthol, a-pinene, b-pinene, and thymol were assayed against the human pathogenic bacteria Bacillus subtilis, Enterobacter cloacae, Escherichia coli O157:H7, Micrococcus flavus, Proteus mirabilis, Pseudomonas aeruginosa, Salmonella enteritidis, S. epidermidis, S. typhimurium, and Staphylococcus aureus. The highest and broadest activity was shown by O. vulgare oil. Carvacrol had the highest antibacterial activity among the tested components.     

Mirror and synchronous couplings of geometric Brownian motions

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in general even if the geometric Brownian motions are martingales. On the other hand, we prove that in the cases of the ergodic average and the infinite time horizon criteria, the mirror coupling and the synchronous coupling are always optimal for general (possibly non-martingale) geometric Brownian motions. We show that the two couplings are efficient if and only if they are optimal over a finite time horizon and give a conjectural answer for the efficient couplings when they are suboptimal.     

Determination of gun propellants erosivity: Experimental and theoretical studies

Requirements for higher and higher performances of contemporary guns intensify investigations concerning influence of various factors on barrel erosion. The most important parameter for the life of the gun is the type of the gun propellant. The device based on modification of 37 mm M39 gun for investigating influence of gun propellant on barrel erosion is used. The nozzle (main part of device) mass loss during firing was the measure of gun propellant erosivity. The theory of nozzle erosion includes basic thermal, chemical and metallurgical factors. The main thermal and chemical factors are maximum nozzle inside surface temperature and gun propellant composition. The maximum nozzle surface temperature was determined theoretically by developed interior ballistic model with heat transfer, and experimentally by micro thermocouples measurements and solution of inverse heat conduction problem. The coefficients of gun propellants erosivity are determined in experimental and theoretical way.     

Quasi-contraction on a cone metric space

In this work we define and study quasi-contraction on a cone metric space. For such a mapping we prove a fixed point theorem. Among other things, we generalize a recent result of H. L. Guang and Z. Xian, and the main result of ?iri? is also recovered.     

Sustainable Synthesis of Chiral Tetrahydrofurans through the Selective Dehydration of Pentoses

L ‐Arabinose is an abundant resource available as a waste product of the sugar beet industry. Through use of a hydrazone‐based strategy, L ‐arabinose was selectively dehydrated to form a chiral tetrahydrofuran on a multi‐gram scale without the need for protecting groups. This approach was extended to other biomass‐derived reducing sugars and the mechanism of the key cyclization investigated. This methodology was applied to the synthesis of a range of functionalized chiral tetrahydrofurans, as well as a formal synthesis of 3R‐3‐hydroxymuscarine.