A note on the integral trace form in cyclotomic fields

Let m >= 3 be an integer, zeta(m) is an element of C a primitive mth root of unity, and K-m the cyclotomic field Q(zeta(m)). An explicit description of the integral trace form Tr-Km/Q(x (x) over bar)vertical bar Z[zeta(m)] where (x) over bar is the complex conjugate of x is presented. In the case where m is prime, a procedure for finding the minimum of the form subject to x being a nonzero element of a certain Z- module in Z[zeta(m)] is presented.

Representação geométrica em Q(zeta_pq)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Forma traço sobre algumas extensões galoisianas de corpos p-Ádicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cúbicas galoisianas

Pós-graduação em Matemática - IBILCE

Corpos cujo condutor é potência de primo: caracterização e reticulados ideais associados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Torres de extensões abelianas de grau primo ímpar não ramificado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Trace, a novel and exegesis

Trace concerns writing-walking and walking-writing. The multiple voices of both novel and exegesis assemble a rhizomic map of a walk and create a never-entirely-certain wandering look upon a woman walking, rather than a single cocksure gaze. Trace explores the aesthetics of Western walking literature and the various nostalgias inherent in that tradition. Trace wonders how lost a character can become on a walk and whether a walk is itself a kind of becoming. In the undefined liminal space where the urban bleeds into the rural, Trace challenges the singular perspective of the dominating gaze with a wandering look, which aims to make an original contribution to both the walk in literature and to exegetical form.

Multiple iterations : mapping the trace

This paper explores the concept that individual dancers leave traces in a choreographer’s body of work and similarly, that dancers carry forward residue of embodied choreographies into other working processes. This presentation will be grounded in a study of the multiple iterations of a programme of solo works commissioned in 2008 from choreographers John Jasperse, Jodi Melnick, Liz Roche and Rosemary Butcher and danced by the author. This includes an exploration of the development by John Jasperse of themes from his solo into the pieces PURE (2008) and Truth, Revised Histories, Wishful Thinking and Flat Out Lies (2009); an adaptation of the solo Business of the Bloom by Jodi Melnick in 2008 and a further adaptation of Business of the Bloom by this author in 2012. It will map some of the developments that occurred through a number of further performances over five years of the solo Shared Material on Dying by Liz Roche and the working process of the (uncompleted) solo Episodes of Flight by Rosemary Butcher. The purpose is to reflect back on authorship in dance, an art form in which lineages of influence can often be clearly observed. Normally, once a choreographic work is created and performed, it is archived through video recording, notation and/or reviews. The dancer is no longer called upon to represent the dance piece within the archive and thus her/his lived presence and experiential perspective disappears. The author will draw on the different traces still inhabiting her body as pathways towards understanding how choreographic movement circulates beyond this moment of performance. This will include the interrogation of ownership of choreographic movement, as once it becomes integrated in the body of the dancer, who owns the dance? Furthermore, certain dancers, through their individual physical characteristics and moving identities, can deeply influence the formation of choreographic signatures, a proposition that challenges the sole authorship role of the choreographer in dance production. This paper will be delivered in a presentation format that will bleed into movement demonstrations alongside video footage of the works and auto-ethnographic accounts of dancing experience. A further source of knowledge will be drawn from extracts of interviews with other dancers including Sara Rudner, Rebecca Hilton and Catherine Bennett.

Trace element nutrition of the silkwormBombyx mori L. II. Relationship between cobalt, vitamin B12, benzimidazole and purines

Benzimidazole is toxic to silkworms due to its antagonistic action to purines. Cobalt and copper possess the capacity to reverse its toxicity because of their ability to form complexes with benzimidazole. For reasons unknown cobalt exerts a favourable effect in its free form rather than in the vitamin form on the insect growth.

Form, Content, and Magnetism in Iron Oxide Nanocrystals

Monodisperse iron oxide nanocrystals with spherical and cubic morphologies, of comparable dimensions, have been prepared by the thermal decomposition of FeOOH. The lattice spacings of both forms agree with that of magnetite, Fe(3)O(4). The two, however, exhibit very different blocking temperatures. Nanocrystals of cubic morphology are superparamagnetic above 190 K while the spherical nanocrystals at a lower temperature, 142 K. The higher blocking temperatures in particles of cubic morphology are shown to be a consequence of exchange bias fields. We show that in the present iron oxide nanocrystals the exchange bias fields originate from the presence of trace amounts of wustite, FeO. A Reitveld refinement analysis of the X-ray diffraction patterns shows that nanocrystals of cubic morphology have a higher FeO content. The higher FeO content is responsible for the larger exchange bias fields that in turn lead to a higher blocking temperature for nanocrystals with cubic morphology.

Tracing a Crystallization Pathway of an RT Liquid, 4-Fluorobenzoyl Chloride: Metastable Polytypic Form as an Intermediate Phase

When quenched with liquid N-2, a room temperature liquid, 4-fluorobenzoyl chloride, generates a new crystalline form that appears to be polytypic to the previously reported form. The structural and energetic correlations between these forms trace a crystallization pathway of the compound.

Trace metals -- a potential threat to our fishing industry

Trace metals constitute a major form of water pollutant that can adversely affect fish production. The potentially toxic metals have been identified as lead, zinc, copper, arsenic, antimony, mercury beryllium, barium, cadmium, chromium, nickel, selenium among others. Preliminary laboratory studies have been directed to the determination of traces of lead in the aquatic biota and its toxicity. There are indications that the levels reported in effluents from some of the industries may be above the tolerant limits of local fish species and organisms that make up their food. Metal pollution could become a serious problem to freshwater fisheries in the future as a result of increasing urbanization and industrialization, unless efforts are made to prevent it

Speciation of some trace metals (Fe, Cu, and Cd) in El-Mex Bay waters, Alexandria, Egypt

Surface- and bottom-water samples were collected from October 1996 to August 1997 to study levels of iron, copper, and cadmium species in their dissolved labile as well as non-labile and particulate forms in the waters of El-Mex Bay. The results showed that the non-labile concentration of the metals was generally more abundant than that of the labile form: its content reached more than 90% of the total dissolved metal for Cu and more than 80% for Fe. The particulate form was almost at the level of the labile form. The annual concentration of the trace metals of the labile form was 13 µglˉ¹ for Fe; 3µglˉ¹ for Cu, and 1.2 µglˉ¹ for Cd in the surface- and bottom-waters.

Promoting carbonization of polypropylene during combustion through synergistic catalysis of a trace of halogenated compounds and Ni2O3 for improving flame retardancy

The effect of combination between a trace of halogenated compounds (such as ferric chloride and ammonium bromide) and Ni2O3 particles on the carbonization of polypropylene (PP) was investigated during combustion. The results showed a synergistic catalysis of combined halogenated compounds with Ni2O3 in promoting the formation of the residual char during combustion. The investigation on the promotion mechanism showed that halide radical releasing from halogen-containing additives worked as a catalyst to accelerate dehydrogenation-aromatization of degradation products of PR which promote the degradation products to form the residual char catalyzed by nickel catalyst.

Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.