Lie algebroid structures on double vector bundles and representation theory of Lie algebroids

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.     

Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.     

Rotational disorder in 1,5-dihydroxy xanthone

The crystal structure of 1,5-dihydroxy xanthone obtained from Callophyllum trapezifolium has been determined (C₁₃H₈O₄), Mr = 228.21, a = 5.547(5), b = 5.186(5), c = 16.487(5) Å, = 91.40(1), Z = 2 and V = 474.1(6) ų. The xanthone molecule is planar and exhibits rotational disorder in the crystal. The packing of the molecules in the crystal lattice is due to inter- and intramolecular O–H O hydrogen bonds forming infinite chains.     

Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers

This paper studies a facility location problem with stochastic customer demand and immobile servers. Motivated by applications to locating bank automated teller machines (ATMs) or Internet mirror sites, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. Customers are assumed to visit the closest open facility. The objective of this problem is to minimize customers' total traveling cost and waiting cost. In addition, there is a restriction on the number of facilities that may be opened and an upper bound on the allowable expected waiting time at a facility. Three heuristic algorithms are developed, including a greedy-dropping procedure, a tabu search approach and an -optimal branch-and-bound method. These methods are compared computationally on a bank location data set from Amherst, New York.     

Dip-pen nanolithography of reactive alkoxysilanes on glass

The use of organofunctional silane chemistry is a flexible and general method for immobilizing biomolecules on silicon oxide surfaces, including fabricating DNA, small-molecule, and protein microarrays. The biggest hurdle in employing dip-pen nanolithography (DPN) for extending this general approach to the nanoscopic domain is the tendency of trialkoxy- and trichlorosilanes to rapidly polymerize due to hydrolysis reactions. The control of the local water concentration between the substrate surface and the scanning AFM tip is critical, both to the physical and chemical processes involved in DPN writing and to the ability to form well-defined thin layers of reactive silanes without extensive polymerization induced disorder. We found that we could control the degree of polymerization through careful choice of the alkoxysilane used as the "ink" for DPN and through control of the relative humidity during inking and writing with the coated AFM tip. As a proof-of-principle, we demonstrate that areas patterned with an alkoxysilane on glass with DPN are functional for subsequent immobilization of fluorescently labeled streptavidin via covalent attachment of biotin. This preliminary result sets the stage for the ability to capture proteins in their fully hydrated state from buffered solution, by molecular recognition onto previously written reactive nanoscopic regions on oxidized silicon and glass.     

An unusual mechanism of glycoside hydrolysis involving redox and elimination steps by a family 4 beta-glycosidase from Thermotoga maritima

Among the numerous well-characterized families of glycosidases, family 4 appears to be the anomaly, requiring both catalytic NAD+ and a divalent metal for activity. The unusual cofactor requirement prompted the proposal of a mechanism involving key NAD+-mediated redox steps as well as elimination of the glycosidic oxygen. Primary kinetic isotope effects for the 2- and 3-deutero substrate analogues, isotopic exchange with solvent, and structural analysis of a 6-phospho-beta-glucosidase, BglT (E.C. 3.2.1.6), provided evidence in support of the proposed mechanism, which has striking resemblances to that of the sugar dehydratases. Furthermore, analysis of the stereochemical outcome indicated that family 4 enzymes are retaining glycosidases.     

The non-aqueous polymerisation of N-vinylpyrrolidone in the presence of poly(acrylic acid)

In order to overcome the hydrolysis of monomer when polymerisation of N-vinylpyrrolidone is attempted in aqueous solution in the presence of polyacrylic acid and potassium per sulphate, the reaction was carried out in dimethylformamide. Two distinct regions in the polymerisation were observed, corresponding to the first five minutes of the reaction and to the later stages. In both, a template effect could be observed, a maximum in rate occurring as the concentration of the polyacrylic acid was increased. The reaction appeared to be very much faster in the initial stages. The orders with respect to monomer and initiator were found.     

Crystal structure of nimbin

The crystal structure of nimbin has been determined. The crystals are orthorhombic, space groupP2₁2₁2₁ witha=6.790(2),b=14.875(4),c=27.160(8) Å andZ=4. The packing of the molecules in the lattice is due to C?H…O type of hydrogen bonds.     

Regularized Lardy Scheme for Solving Singularly Perturbed Elliptic and Parabolic PDEs

Mediterranean Journal of Mathematics - In the present paper, we introduce screen generic lightlike submanifold of golden semi-Riemannian manifolds and give non-trivial examples of such...