7 resultados para ALMOST-PERIODIC SOLUTIONS

em Brock University, Canada


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Modifications to the commercial hydride generator, manufactured by Spectrametrics, resulted in improved operating procedure and enhancement of the arsenic and germanium signals. Experiments with arsenic(III) and arsenic(V) showed that identical reiults could be produced from both oxidation states. However, since arsenic(V) is reduced more slowly than arsenic(III), peak areas and not peak heights must be measured when the arsine is immediately stripped from the system (approximately 5 seconds reaction). When the reduction is allowed to proceed for 20 seconds before the arsine is stripped, peak heights may be used. For a 200 ng/mL solution, the relative standard deviation is 2.8% for As(III) and 3.8% for As(V). The detection limit for arsenic using the modified system is 0.50 ng/mL. Studies performed on As(V) standards show that the interferences from 1000 mg/L of nickel(II), cobalt(II), iron(III), copper(II), cadmium(II), and zinc(II) can be eliminated with the aid of 5 M Hel and 3% L-cystine. Conditions for the reduction of germanium to the corresponding hydride were investigated. The effect of different concentrations of HCl on the reduction of germanium to the covalent hydride in aqueous media by means of NaBH 4 solutions was assessed. Results show that the best response is accomplished at a pH of 1.7. The use of buffer solutions was similarly characterized. In both cases, results showed that the element is best reduced when the final pH of the solution after reaction is almost neutral. In addition, a more sensitive method, which includes the use of (NH4)2S208' has been developed. A 20% increase in the germanium signal is registered when compared to the signal achieved with Hel alone. Moreover, under these conditions, reduction of germanium could be accomplished, even when the solution's pH is neutral. For a 100 ng/mL germanium standard the rsd is 3%. The detection limit for germanium in 0.05 M Hel medium (pH 1.7) is 0.10 ng/mL and 0.09 ng/mL when ammonium persulphate is used in conjunction with Hel. Interferences from 1000 mg/L of iron(III), copper(II), cobalt(II), nickel(II), cadmium(II), lead(II), mercury(II), aluminum(III), tin(IV), arsenic(III), arsenic(V) and zinc(II) were studied and characterized. In this regard, the use of (NH4)ZS20S and Hel at a pH of 1.7 proved to be a successful mixture in the sbppression of the interferences caused by iron, copper, aluminum, tin, lead, and arsenic. The method was applied to the determination of germanium in cherts and iron ores. In addition, experiments with tin(IV) showed that a 15% increase in the tin signal can be accomplished in the presence of 1 mL of (NH4)2S20S 10% (m/V).

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Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

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This work contains the results of a series of reduction studies on polyhalogenated aromatic compounds and related ethers using alkali metals in liquid ammonia. In general, polychlorobenzenes were reduced to t he parent aromatic hydrocarbon or to 1 ,4-cyc1ohexadiene, and dipheny1ethers were cleaved to the aroma tic hydrocarbon and a phenol. Chlorinated dipheny1ethers were r eductive1y dechlorinated in the process. For example, 4-chlorodipheny1- ether gave benzene and phenol. Pentach1orobenzene and certain tetrachlorobenzenes disproportionated to a fair degree during the reduction process if no added proton source was present. The disproportionation was attributed to a build-up of amide ion. Addition of ethanol completely suppressed the formation of any disproportionation products. In the reductions of certain dipheny1ethers , the reduction of one or both of the dipheny1ether rings occurred, along with the normal cleavage. This was more prevalent when lithium was the metal used . As a Sidelight, certain chloropheno1s were readily dechlorinated. In light of these results, the reductive detoxification of the chlorinated dibenzo-1,4-dioxins seems possible with alkali metals in l iquid ammonia.

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The general solution behaviour and" the major fragmentation pathways of the anticanceractive PtIV coordination complexes, trans, trans, cis, cis-[PtCIOH{N(pFC6F4) CH2h(pY)2] (1), trans, cis, cis-[Pt(OH)2{N(p-FC6F4)CH2h(Py)2] (2), trans, cis, cis-[Pt(OH)2{N(p-HC6F4)CH2h(Py)2] (3), trans, trans, cis, cis-[PtCIOH{N(pHC6F4) CH2h(Py)2] (4), and trans, trans, cis, cis-[PtOH(OCH3){N(p-HC6F4)CH2h(PY)2] (5) (Py = pyridine) have been deduced by positive-ion tandem-in-time ESI-MS. Overall, the acquired full-scan, positive-ion ESI-MS spectra of 2, 3, and 5 were characterized by the presence of relatively low-intensity [M+Nar and [M+Kt mass spectral peaks, whereas those of 1 and 4 were dominated by extremely intense [M+Hr peaks. Complexes 2 and 3 were also noted to form [2M+Ht and [2M+Nat dilneric cations. The source of Na + and K+ ions is believed to be the sample, the solvent systems used or the transport line carrying the sample solutions into the ES ion source. Further, the fragmentation pathway of all complexes studied was found to be almost identical with concurrent loss of py and H20 molecules, loss of a {N(p-YC6F4)CH2} (Y = F, H) group and/or concomitant release of the latter group and a py ligand being the most conunon. The photochemical degradation behaviour of 1 and 2 was also investigated using either fluorescent or ultraviolet light and some products of that degradation were positively identified. Altogether, light irradiation of solutions of both complexes resulted in cation cationisation, reductive-elimination, ligand-release, ligand-exchange and ligand-addition reactions. Finally, positive- and negative-ion ESI-MSn spectra of 5' -GMP, guanosine, inosine and products of their reactions with 1, 2,3, and 4 were also recorded. On the whole, full-scan ESI-MS spectra of the pure nucleobases revealed the presence of cationic and anionic species that are highly reflective of both their solution ionic composition and their propensity t9 form polymeric clusters. Analyses of mass spectra acquired from their reaction solutions with the aforementioned platinum complexes indicated very slow kinetics. However, all complexes investigated formed, to various degrees, Pt-nucleobase adducts with guanosine and inosine, but not with 5'-GMP. The products included species having coordination numbers of III, IV, V, and VI, among which the first-time· observed, coordinatively saturated, jive-coordinate PtlI-nucleobase complexes were of most interest. The latter complexes are presumably stabilized by 7tback- donation involving the filled d orbitals of the PtII centre and the empty pz· orbital of MeCN. All products, whose peaks appeared inlull-scan ESI-MS spectra, are believed to represent solution species rather than artifacts of gas-phase processes. Finally, negativeion ESI-MSn spectra recorded in reaction solutions of 1 and 4 with guanosine and of the latter complex with inosine revealed the negative-ion-ESI-MS first-time observed, noncovalent, nucleoside-chloride adducts, with the source of chloride anion being complexes 1 and 4 theillselves. In contrast, no such adducts were observed to form with Na25'-GMP or its protonated fonn. Few suggestions are offered for the possible cause(s) behind the absence of such adduct ions.

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In this paper we study the extended Tanh method to obtain some exact solutions of KdV-Burgers equation. The principle of the Tanh method has been explained and then apply to the nonlinear KdV- Burgers evolution equation. A finnite power series in tanh is considered as an ansatz and the symbolic computational system is used to obtain solution of that nonlinear evolution equation. The obtained solutions are all travelling wave solutions.

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Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.