Ab initio calculation of the effective valence shell hamiltonian of carbon: Simultaneous treatment of neutral and ion states

The n = 2 effective valence shell hamiltonian, $\text{H}$^v, of carbon is evaluated through second order using ³P Hartree—Fock orbitals (5s4p) with added d functions to provide results within a few percent of the spd convergence limits. The calculated $\text{H}$^v is employed to evaluate the n = 2 valence states of C, C^?, C⁺, C²⁺ and C³⁺ with an average deviation of the 21 excitation energies, ionization potentials and electron affinity from experimental values of 0.32 eV. Three-electron parts of $\text{H}$^v contribute substantially to a number of these excitation energies.     

Quasi 3D imaging of DNA-gold nanoparticle tetrahedral structures

Verification by imaging of the structure of 3D DNA constructs, both bare and conjugated to metal nanoparticles, is challenging. We demonstrate here two transmission electron microscopy (TEM) based methods to distinguish between fully formed tetrahedra, synthesized from DNA conjugated with gold nanoparticles (GNPs) at their vertices, and structures which are only partially formed. When deposited on a surface, fully formed tetrahedra are expected to retain their 3D pyramidal structure, while partially formed structures are expected to form a 2D structure. The first method by which 3D and 2D structures were distinguished was imaging them at different defocusing values. While for 2D structures all the four GNPs acquire Fresnel fringes at the same defocusing value, for 3D structures at least one particle is at a different plane with respect to the others, and so it acquires Fresnel fringes at a different defocusing value. The second method we show is imaging of the structures at different angles. While a single TEM image gives only a 2D projection of the structure, by combining information achieved from imaging at several tilting angles one may verify the structural construct.     

Optimally Computing the Shortest Weakly Visible Subedge of a Simple Polygon

Given ann-vertex simple polygonP, the problem of computing the shortest weakly visible subedge ofPis that of finding a shortest line segmentson the boundary ofPsuch thatPis weakly visible froms(ifsexists). In this paper, we present new geometric observations that are useful for solving this problem. Based on these geometric observations, we obtain optimal sequential and parallel algorithms for solving this problem. Our sequential algorithm runs inO(n) time, and our parallel algorithm runs inO(log n) time usingO(n/log n) processors in the CREW PRAM computational model. Using the previously best known sequential algorithms to solve this problem would takeO(n²) time. We also give geometric observations that lead to extremely simple and optimal algorithms for solving, both sequentially and in parallel, the case of this problem where the polygons are rectilinear.     

Essential concepts in the optical properties of quantum dot molecules

Here we review the basic optical spectra of quantum dot molecules. We apply a simple and straightforward model to calculate charge stability regions in vertically coupled double dot molecules that are embedded in a Schottky diode. This model allows us to relate features in the optical spectrum to the diode structure. The underlying concepts allow one to design quantum dot molecules functionalized for optical operations.     

Chern Character in Twisted K-Theory: Equivariant and Holomorphic Cases

 It was argued in [25, 5] that in the presence of a nontrivial B-field, D-brane charges in type IIB string theories are classified by twisted K-theory. In [4], it was proved that twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose elements are ordinary Hilbert bundles on a principal projective unitary bundle, with an action of the bundle gerbe determined by the principal projective unitary bundle. The principal projective unitary bundle is in turn determined by the twist. This paper studies in detail the Chern-Weil representative of the Chern character of bundle gerbe K-theory that was introduced in [4], extending the construction to the equivariant and the holomorphic cases. Included is a discussion of interesting examples. Received: 10 January 2002 / Accepted: 9 December 2002 Published online: 25 February 2003 RID="⋆" ID="⋆" The authors acknowledge the support of the Australian Research Council Communicated by R.H. Dijkgraaf     

Australian Honeypot Ant (Camponotus inflatus) Honey—A Comprehensive Analysis of the Physiochemical Characteristics,Bioactivity, and HPTLC Profile of a Traditional Indigenous Australian Food

Despite its cultural and nutritional importance for local Aboriginal people, the unusual insect honey produced by Western Australian honeypot ant (Camponotus inflatus) has to date been rarely investigated. This study reports on the honey’s physicochemical properties, its total phenolic, major sugars and 5-hydroxymethylfurfural contents, and its antioxidant activities. The honey’s color value is 467.63 mAU/63.39 mm Pfund, it has a pH of 3.85, and its electric conductivity is 449.71 µSiemens/cm. Its Brix value is 67.00, corresponding to a 33% moisture content. The total phenolics content is 19.62 mg gallic acid equivalent/100 g honey. Its antioxidant activity measured using the DPPH* (2,2-diphenyl-1-picrylhydrazyl) and FRAP (ferric reducing–antioxidant power) assays is 1367.67 µmol Trolox/kg and 3.52 mmol Fe⁺²/kg honey, respectively. Major sugars in the honey are glucose and fructose, with a fructose-to-glucose ratio of 0.85. Additionally, unidentified sugar was found in minor quantities.     

The algebraic structure of cohomological field theory

The algebraic foundation of cohomological field theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occuring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.     

Hill‐climbing to Pasch valleys

Exhaustive enumeration of Steiner Triple Systems is not feasible, due to the combinatorial explosion of instances. The next‐best hope is to quickly find a sample that is representative of isomorphism classes. Stinson's Hill‐Climbing algorithm [ 20 ] is widely used to produce random Steiner Triple Systems, and certainly finds a sample of systems quickly, but the sample is not uniformly distributed with respect to the isomorphism classes of STS with ν ≤ 19, and, in particular, we find that isomorphism classes with a large number of Pasch configurations are under‐represented. No analysis of the non‐uniformity of the distribution with respect to isomorphism classes or the intractability of obtaining a representative sample for ν > 19 is known. We also exhibit a modification to hill‐climbing that makes the sample if finds closer to the uniform distribution over isomorphism classes in return for a modest increase in running time. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 405–419, 2007