Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Visualização das funções complexas e do Teorema Fundamental da Álgebra

Pós-graduação em Matemática Universitária - IGCE

A note on the hypercomplex riemann-cauchy like relations for quaternions and laplace equations

In this Note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier [1]. As in the theory of functions of a complex variable, it is expected that this new set of Laplace-Like equations might be applied to a large number of Physical problems, providing new insights in the Classical Fields Theory.

Variable parameter and double sampling (X)over-bar charts in the presence of correlation: The Markov chain approach

The general assumption under which the (X) over bar chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the (X) over bar chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the (X) over bar chart. The performance of the chat (X) over bar with variable parameters and the (X) over bar with double sampling are compared. (C) 2011 Elsevier B.V. All rights reserved.

Lobe identity in the Mongolian gerbil prostatic complex: A new rodent model for prostate study

Knowledge of structural and physiological differences among the prostatic lobes (PL) is the basis for development of experimental studies in traditional laboratory rodents. Although Mongolian gerbil reproductive organs have been increasingly investigated, its prostate structure is far from being properly known, and investigations of this organ focused on the ventral lobe (VL). Thus, the present study provides a thorough morphological description of prostatic complex in the male adult gerbil on the basis of topographic, histological, and ultrastructural analysis and ductal branching. Like other rodents, four pairs of PL were observed. However, in contrast to the rat and mouse, the VL is the least voluminous component and the dorsolateral lobe (DLL) is the most prominent and spatially isolated from remaining PL. The occurrence of a dorsal lobe (DL), hidden between bladder and insertion of seminal vesicles, has not been mentioned in previous reports with Mongolian gerbil. Collagenase digestion followed by microdissection revealed that, except for DL, which has a tubularacinar organization, all PL exhibit tubular organization and variable ductal branching. Distinct histological and ultrastructural features such as secretory epithelium, aspect of luminal secretion and stromal organization are reported for each PL and are confirmed by morphometric and stereological methods. Histological sections showed at least three intralobar segments in VL and DL. Ultrastructural analysis evidenced that, although luminal epithelial cells of PL share typical features of exocrine secretory cells, there are striking lobe phenotypical variations. Both merocrine and apocrine pathways are observed in variable rates in all PL, with the predominance of the former in the DLL and the latter in the CG. The morphological observations presented herein point to distinct structural identities for each PL, which probably reflects,specific functional compromise of seminal fluid secretion. These data also point to the gerbil as a good model for investigations concerning the regulation of prostate development and homeostasis, mainly with regard to the dorsal and dorsolateral PL.

Financial comparisons of the artisanal fisheries in Urubupungá Complex in the middle Paraná River (Brazil)

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

Group size and composition of Guiana dolphins (Sotalia guianensis) (Van Bénèden, 1864) in the Paranaguá Estuarine Complex, Brazil

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

Assessing the above-ground biomass of a complex tropical rainforest using a canopy crane

Current estimates of the total biomass in tropical rainforests vary considerably; this is due in large part to the different approaches that are used to calculate biomass. In this study we have used a canopy crane to measure the tree architectures in a 1 ha plot of complex mesophyll vine forest at Cape Tribulation, Australia. Methods were developed to measure and calculate the crown and stem biomass of six major species of tree and palm (Alstonia scholaris (Apocynaceae), Cleistanthus myrianthus (Euphorbiaceae), Endiandra microneura (Lauraceae), Myristica insipida (Myristicaceae), Acmena graveolens (Myrtaceae), Normanbya normanbyi (Arecaceae)) using the unique access provided by the crane. This has allowed the first non-destructive biomass estimate to be carried out for a forest of this type. Allometric equations which relate tree biomass to the measured variable 'diameter at breast height' were developed for the six species, and a general equation was also developed for trees on the plot. The general equation was similar in form to equations developed for tropical rainforests in Brazil and New Guinea. The species equations were applied at the level of families, the generalized equation was applied to the remaining species which allowed the biomass of a total of 680 trees to be calculated. This has provided a current estimate of 270 t ha-1 above-ground biomass at the Australian Canopy Crane site; a value comparable to lowland rainforests in Panama and French Guiana. Using the same tree database seven alternative allometric equations (literature equations for tropical rainforests) were used to calculate the site biomass, the range was large (252-446 t ha-1) with only three equations providing estimates within 34 t ha-1 (12.5%) of the site value. Our use of multiple species-specific allometric equations has provided a site estimate only slightly larger (1%) than that obtained using allometric equations developed specifically for tropical wet rainforests. We have demonstrated that it is possible to non-destructively measure the biomass in a complex forest using an on-site canopy crane. In conjunction the development of crown maps and a detailed tree architecture database allows changes in forest structure to be followed quantitatively. © 2007 Ecological Society of Australia.

Complex Call with Different Messages in Bokermannohyla ibitiguara (Anura, Hylidae), a Gladiator Frog of the Brazilian Cerrado

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variable assessment of wing colouration in aerial contests of the red-winged damselfly Mnesarete pudica (Zygoptera, Calopterygidae)

Wing pigmentation is a trait that predicts the outcome of male contests in some damselflies. Thus, it is reasonable to suppose that males would have the ability to assess wing pigmentation and adjust investment in a fight according to the costs that the rival may potentially impose. Males of the damselfly Mnesarete pudica exhibit red-coloured wings and complex courtship behaviour and engage in striking male– male fights. In this study, we investigated male assessment behaviour during aerial contests. Theory suggests that the relationship between male resource-holding potential (RHP) and contest duration describes the kind of assessment adopted by males: self-assessment, opponent-only assessment or mutual assessment. A recent theory also suggests that weak and strong males exhibit variations in the assessment strategies adopted. We estimated male RHP through male body size and wing colouration (i.e. pigmentation, wing reflectance spectra and transmission spectra) and studied the relationship between male RHP and contest duration from videodocumented behavioural observations of naturally occurring individual contests in the field. The results showed that males with more opaque wings and larger red spots were more likely to win contests. The relationships between RHP and contest durations partly supported the self-assessment and the mutual assessment models. We then experimentally augmented the pigmented area of the wings, in order to evaluate whether strong and weak males assess rivals’ RHP through wing pigmentation. Our experimental manipulation, however, clearly demonstrated that strong males assess rivals’ wing pigmentation. We finally suggest that there is a variation in the assessment strategy adopted by males

Variable assessment of wing colouration in aerial contests of the red-winged damselfly Mnesarete pudica (Zygoptera, Calopterygidae)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Detection of bla(CTX-M)-type genes in complex class 1 integrons carried by Enterobacteriaceae isolated from retail chicken meat in Brazil

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