Schwartz Method Research Articles

Kinetics of Autocatalytic Oxidation of Mn(II) Ions by Periodate in Relation to Manganese Oscillations

The kinetics of the autocatalytic oxidation of Mn(II) ions by periodate was investigated in unbuffered phosphoric acid solutions and in buffered solutions; the process was studied in a bath reactor in relation to the chemical oscillations in a continuously flow stirred tank reactor (CSTR), which are based on the chemistry of manganese. The rate constants k1 and k'2 corresponding to the noncatalyzed and catalyzed reaction course were determined by the Schwartz method. While MnO4- ions are the reaction product in the unbuffered phosphoric acid medium, in a CH3COOH-NaOH buffer the Mn2+ ions are only oxidized to Mn(IV). For this case, a reaction pathway is discussed where the key step encompasses dimerization of MnO(OH)+ ions followed by the formation of (MnO2)col colloids, stabilized by adsorption of H2PO4- ions on their surface. This reaction pathway is also of importance with respect to the new manganese oscillator which is based on the autocatalytic oxidation of Mn(II) ions by periodate in a CSTR.

Fixation of organic dications by poly(methacrylic acid)

This work refers to interaction between organic dications (diamidines) and poly(methacrylic acid). By the u.v. spectral method, it was discovered that the efficiency of the ion binding and stability of the resulting complexes depend upon the ion power and solution pH. The co-operativity of the ion binding was evaluated by the Schwartz method.

On a modified Schwartz method for solving grid boundary value problems in domains composed of rectangles and rectangular parallelepipeds

Article On a modified Schwartz method for solving grid boundary value problems in domains composed of rectangles and rectangular parallelepipeds was published on January 1, 1990 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 5, issue 1).

Fictitious components method and the modified difference counterpart of the Schwartz method

Fictitious components method and the modified difference counterpart of the Schwartz method

PEROXIDES AS A SOURCE OF ERROR IN THE QUANTITATIVE DETERMINATION OF MONOCARBONYLS IN CHEESE

ABSTRACTIn the study of the monocarbonyl fraction of cheese, the direct derivatization method of Schwartz has been compared with a high vacuum distillation method. Amounts of aldehydes recovered from cheese when using the former method were significantly greater and a complete homologous series of intermediary chain length n‐alkanals (C5‐C10) was only found when using the Schwartz method. Peroxide value determination in the fat before and after percolating the fat extract through the derivatization column showed that during this step an important destruction of peroxides occurred. This suggests that the intermediary chain length n‐alkanals may arise from an acidic scission of unsaturated fatty acid hydroperoxides.

Schwartz's method and Goldstein's eigenvalue problem

The author uses Schwartz's method to study a relativistic problem whose mathematical structure is similar to Goldstein's eigenvalue problem, i.e. the problem of a zero energy Klein-Gordon particle in an external Coulomb field. It is shown that Schwartz's method fails to give a correct answer. The result suggests that additional information about the eigenvalue spectrum for energies different from zero is needed before deciding whether Goldstein's cut-off independent solution discussed recently by Delbourgo and Prasad is physically meaningful.

Vibrational Relaxation of Oxygen

The vibrational relaxation of oxygen has been studied by shock-tube interferometry from 600° to 2600°K with the result that at 1 atm pressure the relaxation time τv in seconds is found to be τv=1.49×10—10 exp (133T—½). The presence of up to 2% CO has no observable effect on this time. The previous experimental work of Blackman was probably influenced by impurities at the lower temperatures but the present results are in accord with his at the higher temperatures. Comparison is made with various theoretical calculations and the primary temperature dependence of T—½ is confirmed. It is further noted that Schwartz's Method A of matching the exponential interaction is in better accord with observations than Method B.

Some Calculations of Observables based on the Schwartz Method

The Schwartz method has been extended to calculations of the x-ray scattering factor, and for the ground state of helium and to for the triplet state of helium, all with good accuracy. It is shown that the Schwartz method fails for a trial wave function that does not satisfy the virial theorem.

173. Note: On Schwartz and Wearden's Method of Estimating Heritability

173. Note: On Schwartz and Wearden's Method of Estimating Heritability

Efficiencies of third bodies in the reaction H + O2+ M = HO2+ M

Vibrational transition probabilities have been calculated by the Schwartz, Slawsky and Herzfeld method [3] for the deactivation of HO2* in collision with H2, O2 and CO2. The relative efficiencies of H2, O2 and CO2 are compared with their third-body efficiencies found experimentally and it is concluded that the transfer of large vibrational quanta from HO2* is unlikely to play an important part in determining the position of the second explosion limit of the H2/O2 reaction. This conclusion is at variance with the explanation put forward by Walsh [1] of the ‘anomalous’ third-body efficiencies of H2O and CO2 in this reaction.