The kinetics of oxidation of thiosulfate to tetrathionate by trans-dihydroxotetraoxoosmate(VIII) in aqueous alkaline media have been studied. The oxidation follows a rate expression where KOs is the formation constant of trans-dihydroxotetraoxoosmate (VIII), and K2 and k3, respectively, represent the formation constants of the intermediate complex involving Os(VIII) and S2O and its decomposition constant. The KOs, K2, and k3 values have been computed to be (19.5 ± 3) dm3/mol, (6.12 ± 0.5) and (3.32 ± 0.3) × 10?1 dm3/mol s at 303 K, and I = 0.32 mol/dm3, respectively. The rate law is consistent with a mechanism envisaging the equilibrium formation of an intermediate complex involving Os(VIII) and S2O, followed by a rate-determining decomposition of the complex with concomitant electron transfer. 相似文献
We generalize Chirkas theorem on the extension of functions holomorphic in a neighbourhood of (F)(D×D) – where D is the open unit disc and (F) is the graph of a continuous D-valued function F – to the bidisc. We extend holomorphic functions by applying the Kontinuitätssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by Chirkas theorem.Mathematics Subject classification (2000): 32D15Work supported by NSF Grant DMS-0072237. 相似文献
The problem considered here is that of fitting a linear function to a set of points. The criterion normally used for this is least squares. We consider two alternatives, viz., least sum of absolute deviations (called the L1 criterion) and the least maximum absolute deviation (called the Chebyshev criterion). Each of these criteria give rise to a linear program. We develop some theoretical properties of the solutions and in the light of these, examine the suitability of these criteria for linear estimation. Some of the estimates obtained by using them are shown to be counter-intuitive. 相似文献
Agostic interactions and weak hydrogen bonds to metal acceptors, M, are chemically and geometrically distinct, and this distinction must be maintained in the classification of new C-H...M interactions. 相似文献
The repetition rate capability of self-switched transversely excited atmosphere (TEA) CO2 laser was studied for different gas flow configurations. For an optimized gas flow configuration, repetitive operation was
achieved at a much smaller gas replenishment factor between two successive pulses when compared with repetitive systems energized
by conventional pulsers. 相似文献
The Cahn–Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn–Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing, then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection–hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection–diffusion equation.
Brent’s method, also known as zeroin, has been the most popular method for finding zeros of functions since it was developed in 1972. This method usually converges very quickly to a zero; for the occasional difficult functions encountered in practice, it typically takes $O(n)$ iterations to converge, where $n$ is the number of steps required for the bisection method to find the zero to approximately the same accuracy. While it has long been known that in theory Brent’s method could require as many as $O(n^2)$ iterations to find a zero, such behavior had never been observed in practice. In this paper, we first show that Brent’s method can indeed take $O(n^2)$ iterations to converge, by explicitly constructing such worst case functions. In particular, for double precision accuracy, Brent’s method takes $2{,}914$ iterations to find the zero of our function, compared to the $77$ iterations required by bisection. Secondly, we present a modification of Brent’s method that places a stricter complexity bound of $O(n)$ on the search for a zero. In our extensive testing, this modification appears to behave very similarly to Brent’s method for all the common functions, yet it remains at worst five times slower than the bisection method for all difficult functions, in sharp contrast to Brent’s method. 相似文献
Formation of a stoichiometric quaternary cocrystal consisting of resorcinol ( RES ), tetramethylpyrazine ( TMP ), phenazine ( PHE ) and pyrene ( PYR ) is described. A closed tetrameric resorcinol‐heterocycle synthon, unusual in that it has two different linker bases rather than just one, is observed in this four‐component solid. The tetrameric synthon is formed by two RES molecules and the two pyridine bases TMP and PHE . The stoichiometric quaternary cocrystal grows in an epitaxial fashion on the surfaces of a RES.PHE binary cocrystal which is initially obtained from the mother liquor. By indexing the common crystal faces of the binary and quaternary cocrystals, and noting that no ternary solid is obtained, a plausible mechanism has been proposed for the formation of this rare supramolecular architecture. 相似文献