Some Normal Cryptogroups as Semigroups of Isomorphisms

Given a Clifford semigroup G, we construct special G-operands L and R which we term conformai. Certain suboperands of L and R we call threads and fix some special G-isomorphisms, which we term coherent, of threads in R onto threads in L. On the set of all coherent G-isomorphisms of threads in L onto threads in R we define a sandwich-type multiplication. When we restrict our threads to be cyclic suboperands of L and R, this construction produces a normal cryptogroup which we represent as $ S=[Y;S_{\alpha},\chi_{{\alpha},{\beta}}] $ -Without any restriction on the threads this produces a semigroup isomorphic with a remarkable ideal of the translational hull of S. Conversely, given a strong semilattice of completely simple semigroups, satisfying certain conditions, we can represent it isomorphically as indicated above.     

A parallel projection method for overdetermined nonlinear systems of equations

We consider overdetermined nonlinear systems of equationsF(x)=0, whereF: ^{n m} ,mn. For this type of systems we define weighted least square distance (WLSD) solutions, which represent an alternative to classical least squares solutions and to other solutions based on residual normas. We introduce a generalization of the classical method of Cimmino for linear systems and we prove local convergence results. We introduce a practical strategy for improving the global convergence properties of the method. Finally, numerical experiments are presented.Work supported by FAPESP (Grant 90/3724/6), FINEP, CNPq and FAEP-UNICAMP.     

Approximation du temps local des surfaces gaussiennes

Summary LetX be a centered stationary Gaussian stochastic process with ad-dimensional parameter (d2),F its spectral measure, (x denotes the Euclidean norm ofx). We consider regularizations of the trajectories ofX by means of convolutions of the formX (t)=( *X)(t) where stands for an approximation of unity (as tends to zero) satisfying certain regularity conditions.The aim of this paper is to recover the local time ofX at a given levelu, as a limit of appropriate normalizations of the geometric measure of theu-level set of the regular approximating processesX . A part of the difficulties comes from the fact that the geometric behavior of the covariance of the Gaussian processX can be a complex one as approaches O.The results are onL ²-convergence and include bounds for the speed of convergence.L ^presults may be obtained in similar ways, but almost sure convergence or simultaneous convergence for the various values ofu do not seem to follow from our methods. In Sect. 3 we have included examples showing a diversity of geometric behaviors, especially in what concerns the dependence on the thickness of the set in which the covariance of the original processX is irregular.Some technical results of analytic nature are included as appendices in Sect. 4.     

Kinetic study of nickel(II) complexation by pteroylglutamic acid

The kinetics of the complexation of NiII by pteroylglutamic acid have been studied in the 545 ∘C range, the ionic strength (0.6 M) being regulated with KNO3, in the 5.5–7.0pH range, using the stopped-flow method. Under the experimental conditions two processes were observed. The faster process was detected in the millisecond range and is associated with the reaction between NiII and the ligand. The slower is observed within a few seconds. Complementary equilibrium studies were made at 25 ∘C. The results are consistent with the formation of a 1:1 complex between the reactants, and a mechanism is proposed to account for the observed behaviour. Equilibrium constants for the NiII plus pteroylglutamic acid system, as well as activation parameters, are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

Reactions of thiosemicarbazones derived from beta-keto amides and beta-keto esters with Zn(II) and Cd(II) acetates: influence of metal, substitution, reagent ratio and temperature on metal-induced cyclization

Zinc(II) and cadmium(II) acetates were reacted in methanol under various experimental conditions with thiosemicarbazones derived from beta-keto amides or beta-keto esters (HTSC). Some of these reactions afforded thiosemicarbazonate complexes [M(TSC)2] with IR and NMR spectra compatible with N,S-coordination, but most gave complexes [ML2], where HL is a substituted 2,5-dihydro-5-oxo-1H-pyrazole-1-carbothioamide resulting from cyclization of the HTSC. Some of these pyrazolonates and two of the HL ligands were studied by X-ray diffractometry, and their structures are discussed. Surprisingly, the reactions of zinc(II) acetate with HTSC in 1:1 mol ratio usually gave a third, previously unreported type of complex with a dideprotonated ligand, [Zn(L-H)], which was also formed when [ZnL2] and Zn(OAc)2 interacted at room temperature in 1:1 mol ratio. These L-H complexes are highly insoluble in all common solvents, which hinders their characterization but suggests that they are polymeric in nature.