3-Phenylisoquinolin-1(2H)-one

The title compound, C15H11NO, consists of a planar isoquinolinone group to which a phenyl ring is attached in a twisted fashion [dihedral angle = 39.44 (4)degrees]. The crystal packing is dominated by intermolecular N-H center dot center dot center dot O and C-H center dot center dot center dot O hydrogen bonds which define centrosymmetric dimeric entitities.

Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

1-(2,4-Dichlorophenyl)-3-[4-(dimethylamino)-phenyl]prop-2-enone

In the title compound, C17H15Cl2NO, the dimethylaminophenyl group is close to coplanar with the central propenone group [dihedral angle =13.1 (1)degrees between the mean planes], while the dichlorophenyl group is twisted from the plane [dihedral angle = 64.0 (1)degrees].In the crystal, C-H center dot center dot center dot O and weak C-H center dot center dot center dot pi interactions are formed between molecules.

Measuring the traction profile on sportsfields: Equipment development and testing

Traction is recognised as an important component of the overall playability and safety of a sportsfield. It relates to the "grip", or footing, provided through an athlete's shoe when in contact with the surface, and is normally measured by the torque generated when a weighted studded disc apparatus is dropped onto the turf and twisted manually. This paper describes the development of an automated traction tester, which mechanises the dropping and twisting of the weighted studded disc. By standardising these operational stages, more repeatable and reliable results can be expected than from the original hand-operated design where positioning of the disc and speed of rotation are controlled manually and so can vary from one measurement to the next. As well as measuring the maximum torque reached during rotation of the studded disc, the automated traction tester generates a profile of torque showing changes over time and calculates the angle through which the studded disc moved before reaching maximum torque. These aspects are now covered by a utility patent (PAT/AU/2004270767). Use of the automated traction tester is illustrated by comparative data for a range of warm-season turfgrasses, by comparisons of traction under different surface conditions generated by wear on Cynodon dactylon cultivars, and by the effects of environment, management and playing patterns on traction across a multi-use sports stadium.

Bibulocystis gloriosa sp nov (Pucciniales) on Caesalpinia scortechinii in Queensland, with comments on Spumula caesalpiniae

A rust causing leaf spotting and distortion of twigs and branches of Caesalpinia scortechinii in Queensland is described as the new species Bibulocystis gloriosa. Uredinia and telia occur on spotted pinnules, and pycnia, aecial uredinia and telia on galled and twisted leaf rachides, twigs and branches. B. gloriosa is similar to Bibulocystis viennotii on Albizia granulosa in New Caledonia in having a macrocyclic life cycle with all spore states, and teliospores with two fertile cells and two cysts. It differs in having aecial urediniospores and urediniospores with uniformly thickened walls and several scattered germ pores, rather than the apically thickened walls and equatorial germ pores of B. viennotii. Teliospores in the two species are similar in size, but those of B. gloriosa have proportionally larger fertile cells and smaller cysts than in B. viennotii. To date, B. gloriosa is known from only two localities in south-eastern Queensland. Comparison with the type specimen of Spumula caesalpiniae on Caesalpinia nuga from Indonesia has shown that the two rusts are generically distinct.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Ethyl 4-(4-chlorophenyl)-6-methyl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate

In the title compound, C14H15ClN2O2S, the tetrahydropyrimidine ring adopts a twisted boat conformation with the carbonyl group in an s-trans conformation with respect to the C C double bond of the six-membered tetrahydropyrimidine ring. The molecular conformation is determined by an intramolecular C-H center dot center dot center dot pi interaction. The crystal structure is further stabilized by intermolecular N-H center dot center dot center dot O molecular chains and centrosymmetric N-H center dot center dot center dot S dimers.

Pi-turns in proteins and peptides: Classification, conformation, occurrence, hydration and sequence.

The i + 5-->i hydrogen bonded turn conformation (pi-turn) with the fifth residue adopting alpha L conformation is frequently found at the C-terminus of helices in proteins and hence is speculated to be a "helix termination signal." An analysis of the occurrence of i + 5-->i hydrogen bonded turn conformation at any general position in proteins (not specifically at the helix C-terminus), using coordinates of 228 protein crystal structures determined by X-ray crystallography to better than 2.5 A resolution is reported in this paper. Of 486 detected pi-turn conformations, 367 have the (i + 4)th residue in alpha L conformation, generally occurring at the C-terminus of alpha-helices, consistent with previous observations. However, a significant number (111) of pi-turn conformations occur with (i + 4)th residue in alpha R conformation also, generally occurring in alpha-helices as distortions either at the terminii or at the middle, a novel finding. These two sets of pi-turn conformations are referred to by the names pi alpha L and pi alpha R-turns, respectively, depending upon whether the (i + 4)th residue adopts alpha L or alpha R conformations. Four pi-turns, named pi alpha L'-turns, were noticed to be mirror images of pi alpha L-turns, and four more pi-turns, which have the (i + 4)th residue in beta conformation and denoted as pi beta-turns, occur as a part of hairpin bend connecting twisted beta-strands. Consecutive pi-turns occur, but only with pi alpha R-turns. The preference for amino acid residues is different in pi alpha L and pi alpha R-turns. However, both show a preference for Pro after the C-termini. Hydrophilic residues are preferred at positions i + 1, i + 2, and i + 3 of pi alpha L-turns, whereas positions i and i + 5 prefer hydrophobic residues. Residue i + 4 in pi alpha L-turns is mainly Gly and less often Asn. Although pi alpha R-turns generally occur as distortions in helices, their amino acid preference is different from that of helices. Poor helix formers, such as His, Tyr, and Asn, also were found to be preferred for pi alpha R-turns, whereas good helix former Ala is not preferred. pi-Turns in peptides provide a picture of the pi-turn at atomic resolution. Only nine peptide-based pi-turns are reported so far, and all of them belong to pi alpha L-turn type with an achiral residue in position i + 4. The results are of importance for structure prediction, modeling, and de novo design of proteins.

2-[2-(Cyclohexylcarbonyl)phenyl]-1-phenylethanone

The title diketone, C21H22O2, features a phenylene ring having benzoylmethyl and cyclohexanoyl substituents ortho to each other. The cyclohexyl ring adopts a chair conformation with the ketonic group occupying an equatorial position; the four-atom -C(O)-C ketonic unit is twisted out of the plane of the phenylene ring by 34.9 (1)degrees.

Ethyl 2,6-dichloro-4-phenylquinoline-3-carboxylate

In the title compound,C18H13Cl2NO2,the quinoline ring system is almost planar (r.m.s.deviation 0.009 angstrom), and the phenyl and carboxylate planes are twisted away from it by 59.2 (1)and 65.9 (2)degrees,respectively.

Ethyl 6-chloro-2-oxo-4-phenyl-1,2-dihydroquinoline-3-carboxylate

In the title compound,C18H14ClNO3,the dihydroquinolin-2-one ring system is almost planar (r.m.s.deviation = 0.033 angstrom).The carboxylate plane and the phenyl group are twisted away from the dihydroquinolin-2-one ring system by 50.3(1) and 64.9(1)degrees,respectively.In the crystal structure, inversion-related molecules form R-2(2)(8)dimers via pairs of N-H center dot center dot center dot O hydrogen bonds.

Harmonic Analysis On Heisenberg Nilmanifolds

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gammakslash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gammakslash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (GammakslashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

5-Phenyl-3-(2-thienyl)-1,2,4-triazolo[3,4-a]isoquinoline

In the title molecule, C20H13N3S, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.045 angstrom and a maximum deviation of 0.090 (2) angstrom from the mean plane for the triazole ring C atom which is bonded to the thiophene ring. The phenyl ring is twisted by 52.0 (1)degrees with respect to the mean plane of the triazoloisoquinoline ring system. The thiophene ring is rotationally disordered by approximately 180 degrees over two sites, the ratio of refined occupancies being 0.73 (1): 0.27 (1).

Adducts of bis(acetylacetonato)zinc(II) with 1,10-phenanthroline and 2,2'-bipyridine

In each of the zinc(II) complexes bis(acetylacetonato-kappa(2)O,O')(1,10-phenanthroline-kappa(2)N,N')zinc(II), [Zn(C(5)H(7)O(2))(2)(C(12)H(8)N(2))], (I), and bis(acetylacetonato-kappa(2)O,O')(2,2'-bipyridine-kappa(2)N,N')zinc(II), [Zn(C(5)H(7)O(2))(2)(C(10)H(8)N(2))], (II), the metal center has a distorted octahedral coordination geometry. Compound (I) has crystallographically imposed twofold symmetry, with Z' = 0.5. The presence of a rigid phenanthroline group precludes intramolecular hydrogen bonding, whereas the rather flexible bipyridyl ligand is twisted to form an intramolecular C-H...O interaction [the chelated bipyridyl ligand is nonplanar, with the pyridyl rings inclined at an angle of 13.4 (1) degrees]. The two metal complexes are linked by dissimilar C-H...O interactions into one-dimensional chains. The present study demonstrates the distinct effects of two commonly used ligands, viz. 1,10-phenanthroline and 2,2'-bipyridine, on the structures of metal complexes and their assembly.