Equações de diferenças e aplicações

Sistemas dinâmicos são todos os sistemas que evoluem no tempo, qualquer que seja a sua natureza, isto é, sistemas fisícos, biológicos, químicos, sociais, económicos, etc.. Esta evoluçãoo pode ser descrita (modelada) por equaçõess de diferenças, uma vez que esse tempo é muitas vezes medido em intervalos discretos. As equações de diferenças aparecem também quando se estuda métodos para a discretização de equações diferenciais. Assim, este trabalho tem por principal objectivo estudar as soluções de alguns tipos de equações de diferenças. Para isso, começa-se por introduzir o conceito de diferença e a sua relação com as equações de diferenças. Em seguida, determina-se a solução geral das todas as equações lineares de primeira ordem, bem como o estudo do seu comportamento assimptótico. Prossegue-se, desenvolvendo as principais técnicas para determinar a soluçãoo de equações de diferenças lineares de qualquer ordem. Em particular, estudam-se as equações com coeficientes constantes. Depois de se desenvolver a teoria básica dos sistemas lineares de equações de diferenças, particulariza-se aos sistemas lineares autónomos,com apenas duas variáveis dependentes, fazendo assim o estudo do comportamento das soluções no plano de fases. Por fim, utiliza-se a transformada Z como uma ferramenta que permite resolver equações de diferenças, em especial as equações de tipo convolução.

Uma fundamentação matemática para processamento digital de sinais intervalares

This work deals with a mathematical fundament for digital signal processing under point view of interval mathematics. Intend treat the open problem of precision and repesention of data in digital systems, with a intertval version of signals representation. Signals processing is a rich and complex area, therefore, this work makes a cutting with focus in systems linear invariant in the time. A vast literature in the area exists, but, some concepts in interval mathematics need to be redefined or to be elaborated for the construction of a solid theory of interval signal processing. We will construct a basic fundaments for signal processing in the interval version, such as basic properties linearity, stability, causality, a version to intervalar of linear systems e its properties. They will be presented interval versions of the convolution and the Z-transform. Will be made analysis of convergences of systems using interval Z-transform , a essentially interval distance, interval complex numbers , application in a interval filter.

Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given

Potassium trifluoro[(Z)-3-methoxyprop-1-enyl]borate

In the title salt, K(+)center dot C(4)H(7)BF(3)O(-), the K atom is surrounded by six anions making close contacts through seven F [K center dot center dot center dot F = 2.779 (1)-3.048 (1) angstrom] and two O [K center dot center dot center dot O = 2.953 (2) and 3.127 (2) angstrom] atoms in a trivacant fac-vIC-9 icosahedral coordination geometry.

Mechanistic aspects of the isomerization of Z-vinylic tellurides double bonds in the synthesis of potassium Z-vinyltrifluoroborate salts

Through direct transmetalation reaction of Z-vinylic tellurides with nBuLi was observed the unexpected isomerization of double bonds leading to potassium E-vinyltrifluoroborates salts in low to moderate yields. Using EPR spin trapping experiments the radical species that promoted the stereoinversion of Z-vinylic organometallic species during the preparation of potassium vinyltrifluoroborate salts was identified. The experiments support the proposed mechanism, which is based on the homolytic cleavage of the TenBu bond.

1-[(Z)-1-Bromo-2-(butyldichloro-lambda(4)tellanyl)ethenyl]cyclohex-1-ene

The Te(IV) atom in the title compound, [Te(C(4)H(9))(C(8)H(10)Br)Cl(2)] or C(12)H(19)BrCl(2)Te, is in a distorted psi-trigonal-bipyramidal geometry, with the lone pair of electrons projected to occupy a position in the equatorial plane, and with the Cl atoms being mutually trans [172.48 (4)degrees]. Close intramolecular [Te center dot center dot center dot Br = 3.3444 (18) angstrom] and intermolecular [Te center dot center dot center dot Cl = 3.675 (3) angstrom] interactions are observed. The latter lead to centrosymmetric dimers which assemble into layers in the bc plane. The primary connections between layers are of the type C-H center dot center dot center dot Cl.

Potassium trifluoro[(Z)-3-(oxan-2-yloxy)prop-1-en-1-yl]borate monohydrate

The title compound, K(+)center dot C(8)H(13)BF(3)O(2)(-)center dot H(2)O, which was obtained from the reaction of a modified form of Z-vinylic telluride via a transmetalation reaction with n-BuLi, crystallizes as K(+) and C(8)H(13)BF(3)O(2)-ions along with a water molecule. The K(+) cation is surrounded by four anions, making close contacts with six F atoms at 2.659 (3)-2.906 (3) angstrom and with two O atoms at 2.806 (3) and 2.921 (3) angstrom in a distorted bicapped trigonal-prismatic geometry.

Cluster and cluster galaxy evolution history from IR to X-ray observations of the young cluster RX J1257.2+4738 at z=0.866

Context. The cosmic time around the z similar to 1 redshift range appears crucial in the cluster and galaxy evolution, since it is probably the epoch of the first mature galaxy clusters. Our knowledge of the properties of the galaxy populations in these clusters is limited because only a handful of z similar to 1 clusters are presently known. Aims. In this framework, we report the discovery of a z similar to 0.87 cluster and study its properties at various wavelengths. Methods. We gathered X-ray and optical data (imaging and spectroscopy), and near and far infrared data (imaging) in order to confirm the cluster nature of our candidate, to determine its dynamical state, and to give insight on its galaxy population evolution. Results. Our candidate structure appears to be a massive z similar to 0.87 dynamically young cluster with an atypically high X-ray temperature as compared to its X-ray luminosity. It exhibits a significant percentage (similar to 90%) of galaxies that are also detected in the 24 mu m band. Conclusions. The cluster RXJ1257.2+4738 appears to be still in the process of collapsing. Its relatively high temperature is probably the consequence of significant energy input into the intracluster medium besides the regular gravitational infall contribution. A significant part of its galaxies are red objects that are probably dusty with on-going star formation.

THE SLOAN BRIGHT ARCS SURVEY: DISCOVERY OF SEVEN NEW STRONGLY LENSED GALAXIES FROM z=0.66-2.94

We report the discovery of seven new, very bright gravitational lens systems from our ongoing gravitational lens search, the Sloan Bright Arcs Survey (SBAS). Two of the systems are confirmed to have high source redshifts z = 2.19 and z = 2.94. Three other systems lie at intermediate redshift with z = 1.33, 1.82, 1.93 and two systems are at low redshift z = 0.66, 0.86. The lensed source galaxies in all of these systems are bright, with i-band magnitudes ranging from 19.73 to 22.06. We present the spectrum of each of the source galaxies in these systems along with estimates of the Einstein radius for each system. The foreground lens in most systems is identified by a red sequence based cluster finder as a galaxy group; one system is identified as a moderately rich cluster. In total, SBAS has now discovered 19 strong lens systems in the SDSS imaging data, 8 of which are among the highest surface brightness z similar or equal to 2-3 galaxies known.

Thermodiffusion in a multicomponent lyotropic mixture in the vicinity of the critical micellar concentration by using the Z-scan technique

Thermodiffusion in a lyotropic mixture of water and potassium laurate is investigated by means of an optical technique (Z scan) distinguishing the index variations due to the temperature gradient and the mass gradients. A phenomenological framework allowing for coupled diffusion is developed in order to analyze thermodiffusion in multicomponent systems. An observable parameter relating to the mass gradients is found to exhibit a sharp change around the critical micellar concentration, and thus may be used to detect it. The change in the slope is due to the markedly different values of the Soret coefficients of the surfactant and the micelles. The difference in the Soret coefficients is due to the fact that the micellization process reduces the energy of interaction of the ball of amphiphilic molecules with the solvent.

Energy transfer upconversion determination by thermal-lens and Z-scan techniques in Nd(3+)-doped laser materials

The Z-scan and thermal-lens techniques have been used to obtain the energy transfer upconversion parameter in Nd(3+)-doped materials. A comparison between these methods is done, showing that they are independent and provide similar results. Moreover, the advantages and applicability of each one are also discussed. The results point to these approaches as valuable alternative methods because of their sensitivity, which allows measurements to be performed in a pump-power regime without causing damage to the investigated material. (C) 2009 Optical Society of America

Cu and Fe metallic ions-mediated oxidation of low-density lipoproteins studied by NMR, TEM and Z-scan technique

In this work we report on a study of the morphological changes of LDL induced in vitro by metallic ions (Cu(2+) and Fe(3+)). These modifications were characterized by transmission electron microscopy, nuclear magnetic resonance and the Z-scan technique. The degree of oxidative modification of LDL was determined by the TBARS and lipid hydroperoxides assays. It is shown that distinct pathways for modifying lipoproteins lead to different morphological transformations of the particles characterized by changes in size and/or shape of the resulting particles, and by the tendency to induce aggregation of the particles. There were no evidence of melting of particles promoted by oxidative processes with Cu and Fe. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Crystal and molecular structures of dichloro((Z)-2-chloro-2-phenylvinyl)(organo)tellurium(IV) for organo = n-butyl and phenyl

In each of the title compounds, R[Ph(Cl)C=(H)C]TeCl(2), R = nBu (1) and Ph (2), the primary geometry about the Te(IV) atom is a pseudo-trigonal-bipyramidal arrangement, with two Cl atoms in apical positions, and the lone pair of electrons and C atoms in the equatorial plane. As the Te(IV) is involved in two, an intra- and an inter-molecular, Te center dot center dot center dot Cl interactions the coordination geometry might be considered as a Psi-pentagonal bipyramid in each case. In addition, in (2) there is a hint of a Te center dot center dot center dot pi interaction (Te center dot center dot center dot C = 3.911(3) A). The key feature in the crystal structure of both compounds is the formation of supramolecular chains mediated by Te center dot center dot center dot Cl contacts. (1): C(12)H(15)Cl(3)Te, triclinic, P (1) over bar, a = 5.9471 (11), b = 10.7826(22), c = 11.7983(19) angstrom, alpha = 75.416(12), beta = 78.868(13), gamma = 80.902(14)degrees, V = 713.6(2) angstrom(3), Z = 2, R(1) = 0.021; (2): C14HIIC13Te, orthorhombic, Pcab, a=7.7189(10), b=17.415(2), c=21.568(3)angstrom, V = 2899.3(6) angstrom(3), Z = 8, R(1) = 0.027.

Structuring real-time Object-Z specifications

This paper presents a means of structuring specifications in real-time Object-Z: an integration of Object-Z with the timed refinement calculus. Incremental modification of classes using inheritance and composition of classes to form multi-component systems are examined. Two approaches to the latter are considered: using Object-Z's notion of object instantiation and introducing a parallel composition operator similar to those found in process algebras. The parallel composition operator approach is both more concise and allows more general modelling of concurrency. Its incorporation into the existing semantics of real-time Object-Z is presented.

The Las Campanas/AAT Rich Cluster Survey - II. The environmental dependence of galaxy colours in clusters at z similar to 0.1

We present a photometric investigation of the variation in galaxy colour with environment in 11 X-ray-luminous clusters at 0.07 less than or equal to z less than or equal to 0.16 taken from the Las Campanas/AAT Rich Cluster Survey. We study the properties of the galaxy populations in individual clusters, and take advantage of the homogeneity of the sample to combine the clusters together to investigate weaker trends in the composite sample. We find that modal colours of galaxies lying on the colour-magnitude relation in the clusters become bluer by d(B - R)/dr(p) = -0.022 +/- 0.004 from the cluster core out to a projected radius of r(p) = 6 Mpc, further out in radius than any previous study. We also examine the variation in modal galaxy colour with local galaxy density, 2, for galaxies lying close to the colour-magnitude relation, and find that the median colour shifts bluewards by d(B - R)/d log(10)(Sigma) = -0.076 +/- 0.009 with decreasing local density across three orders of magnitude. We show that the position of the red envelope of galaxies in the colour-magnitude relation does not vary as a function of projected radius or density within the clusters, suggesting that the change in the modal colour results from an increasing fraction of bluer galaxies within the colour-magnitude relation, rather than a change in the colours of the whole population. We show that this shift in the colour-magnitude relations with projected radius and local density is greater than that expected from the changing morphological mix based on the local morphology-density relation. We therefore conclude that we are seeing a real change in the properties of galaxies on the colour-magnitude relation in the outskirts of clusters. The simplest interpretation of this result (and similar constraints in local clusters) is that an increasing fraction of galaxies in the lower density regions at large radii within clusters exhibit signatures of star formation in the recent past, signatures which are not seen in the evolved galaxies in the highest density regions.