Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Miniaturized membrane sensors for the determination of rivastigmine hydrogen tartrate

Novel miniaturized polyvinyl chloride (PVC) membrane sensors in all-solid state graphite and platinum wire supports were developed, electrochemically evaluated and used for the assay of rivastigmine hydrogen tartrate drug (RIV). The RIV sensors are based on the formation of an ion-association complex between the drug cation and tetrakis(4-chlorophenyl)borate (TpClPB) anionic exchanger as electroactive material dispersed in a PVC matrix. Linear responses of 10(-2) - 10(-5) M and 10(-2) - 10(-4) M with cationic slopes of 56.4 mV and 53.6 mV over the pH range 4 - 7 were obtained by using the RIV-coated graphite (sensor 1) and platinum wire (sensor 2) membrane sensors, respectively. The proposed method displays useful analytical characteristics for the determination of RIV in Exelon capsules with average recoveries of 100.01+/-0.835, 100.09+/-0.896, and in plasma with average recoveries of 99.47+/-0.97, 99.58+/-0.82, and in rat brain homogenate with average recoveries of 98.16+/-1.62, 99.02+/-1.57, for sensors 1 and 2, respectively. The methods were also used to determine the intact drug in the presence of its degradation product and thus could be used as stability indicating methods. The results obtained by the proposed procedures were statistically analyzed and compared with those obtained by using a reported method. No significant difference for both accuracy and precision was observed.     

Analogy between unconventional superconductivity and unconventional states of liquid crystals

An analogy is stressed between the order-parameter symmetries of the two-dimensional d-pairing wave superconductors and of liquid-crystal mesophases formed from achiral bent-shaped molecules. It leads to a definition of a class of liquid-crystal states which are the analogs of the unconventional superconducting states, and are characterized by a loss of discrete symmetry operations of the parent state.     

Membrane electrodes for the determination of glutathione

Four glutathione (GSH)-selective electrodes were developed with different techniques and in different polymeric matrices. Precipitation-based technique with bathophenanthroline-ferrous as cationic exchanger in polyvinyl chloride (PVC) matrix was used for sensor 1 fabrication. β-Cyclodextrin (β-CD)-based technique with either tetrakis(4-chlorophenyl)borate (TpClPB) or bathophenanthroline-ferrous as fixed anionic and cationic sites in PVC matrix was used for fabrication of sensors 2 and 3, respectively.β-CD-based technique with TpClPB as fixed anionic site in polyurethane (Tecoflex) matrix was used for sensor 4 fabrication. Linear responses of 1 × 10⁻⁵ to 1 × 10⁻⁴ M and 1 × 10⁻⁶ to 1 × 10⁻³ M with slopes of 37.5 and 32.0 mV/decade within pH 7-8 were obtained by using electrodes 1 and 3, respectively. On the other hand, linear responses of 1 × 10⁻⁵ to 1 × 10⁻² and 1 × 10⁻⁵ to 1 × 10⁻³ M with slopes of 47.9 and 54.3 mV/decade within pH 5-6 were obtained by using electrodes 2 and 4, respectively. The percentage recoveries for determination of GSH by the four proposed GSH-selective electrodes were 100 ± 1, 100.5 ± 0.7, 100 ± 1 and 99.0 ± 0.8% for sensors 1, 2, 3 and 4, respectively. Determination of GSH in capsules by the proposed electrodes revealed their applicability for determination of GSH in its pharmaceutical formulations. Also, they were used to determine GSH selectively in presence of its oxidized form (GSSG). Sensor 4 was successfully applied for determination of glutathione in plasma with average recovery of 100.4 ± 1.11%. The proposed method was compared with a reported one. No significant difference for both accuracy and precision was observed.     

Search for isovector giant monopole resonances via the Pb(3He,tp) reaction

The (nat)Pb(3He,tp) reaction at E(3He) = 177 MeV was studied to identify 2Planck's over 2piomega isovector monopole strength in Bi isotopes. Monopole strength was found in the region -45相似文献