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.

Synthesis, characterization and biological analysis of the complex [VO(Hdhp)(2)] (H(2)dhp=2,3-dihydroxypyridine)

A new vanadium (IV) complex with the monoanion of 2,3-dihydroxypyridine (H(2)dhp), or 3-hydroxy-2(1H)-pyridone, was synthesized, characterized by physicochemical techniques and tested biologically. The EPR data for the [VO(Hdhp)(2)] complex in DMF are: g(x) = 1.9768, g(y) = 1.9768 and g(z) = 1.9390; A values (10(-4) cm(-1)): A(x), 59.4; A(y//), 59.4; A(z), 171.0. The vV=O band in the IR spectrum of the complex is at 986 cm(-1). The complex is paramagnetic, with mu(eff) = 1.65 BM (d(1), spin-only) at 25 degrees C. The irreversible oxidation process [V(V)/V(IV)] of the [VO(Hdhp)(2)] complex, as revealed in a cyclic voltammogram, occurs at 876 mV. The calculated molecular structure of [VO(Hdhp)(2)] shows the vanadium(IV) center in a distorted square pyramidal environment, with the oxo ligand in the apical position and the oxygen donor atoms of the Hdhp ligands in the basal positions. The ability of [VO(Hdhp)(2)] to mimic insulin, and its toxicity to hepato-biliary functions, were investigated in streptozotocin-induced diabetic rats and it was concluded that the length of treatment and the amount of [VO(Hdhp)(2)] administered were effective in reducing experimental diabetes.

Mapping an uncertainty zone between interpolated types of a categorical variable

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Geometrical logarithmic and trigonometric hypercomplex functions of quaternionic type

Quaternionic theory has greatly been developed in recent years [1-12]. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hyper complex theory. In this paper, we intend to give a geometrical foundation for both logarithmic and trigonometric hyper complex functions based on the exponential function of quaternionic type recently introduced by Borges, Marão and Machado in their paper entitled Geometrical octonions II: Hyper regularity and hyper periodicity of the exponential function appearing. © 2011 Pushpa Publishing House.

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Crystal structure, DNA binding studies, nucleolytic property and topoisomerase I inhibition of zinc complex with 1,10-phenanthroline and 3-methyl-picolinic acid

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wannier functions of isolated bands in one-dimensional crystals

We present a simple procedure to obtain the maximally localized Wannier function of isolated bands in one-dimensional crystals with or without inversion symmetry. First, we discuss the generality of dealing with real Wannier functions. Next, we use a transfer-matrix technique to obtain nonoptimal Bloch functions which are analytic in the wave number. This produces two classes of real Wannier functions. Then, the minimization of the variance of the Wannier functions is performed, by using the antiderivative of the Berry connection. In the case of centrosymmetric crystals, this procedure leads to the Wannier-Kohn functions. The asymptotic behavior of the Wannier functions is also analyzed. The maximally localized Wannier functions show the expected exponential and power-law decays. Instead, nonoptimal Wannier functions may show reduced exponential and anisotropic power-law decays. The theory is illustrated with numerical calculations of Wannier functions for conduction electrons in semiconductor superlattices.

Wannier functions of a one-dimensional photonic crystal with inversion symmetry

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Functional and historical determinants of shape in the scapula of Xenarthran mammals: Evolution of a complex morphological structure

The mammalian scapula is a complex morphological structure, composed of two ossification plates that fuse into a single structure. Most studies on morphological differentiation in the scapula have considered it to be a simple, spatially integrated structure, primarily influenced by the important locomotor function presented by this element. We used recently developed geometric morphometric techniques to test and quantify functional and phylogenetic influences on scapular shape variation in fossil and extant xenarthran mammals. The order Xenarthra is well represented in the fossil record and presents a stable phylogenetic hypothesis for its genealogical history. In addition, its species present a large variety of locomotor habits. Our results show that approximately half of the shape variation in the scapula is due to phylogenetic heritage. This is contrary to the view that the scapula is influenced only by functional demands. There are large-scale shape transformations that provide biomechanical adaptation for the several habits (arboreality, terrestriality, and digging), and small scale-shape transformations (mostly related to the coracoid process) that are not influenced by function. A nonlinear relationship between morphometric and phylogenetic distances indicates the presence of a complex mixture of evolutionary processes acting on shape differentiation of the scapula. J. Morphol. 241,251-263, 1999. (C) 1999 Wiley-Liss, Inc.

Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

The Origin of Nonmonotonic Complex Behavior and the Effects of Nonnative Interactions on the Diffusive Properties of Protein Folding

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

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.