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.     

Terbium sensitized luminescence for the determination of fexofenadine in pharmaceutical formulations

A sensitive and specific luminescence method for the determination of Fexofenadine (FEX), in pharmaceutical formulations is reported. The method is based on the sensitization of terbium (Tb³⁺) by complex formation with FEX. The luminescence signal for Tb–FEX complex is greatly enhanced by the addition of triethylamine (ET₃N) and zinc nitrate in methanol solution. Monitoring of the signal is accomplished when the instrument is in the phosphorescence mode with the excitation and emission wavelengths set at λ_ex = 220 nm and λ_em = 550 nm respectively. Optimum conditions for the formation of the complex in methanol were 2.25 × 10^?6 M of Tb³⁺, 5.00 × 10^?6 M of Et₃N and Zn²⁺ which allows for the determination of 10–800 ppb of FEX in the batch mode with a detection limit of 0.3 ppb. The proposed method was successfully applied for the determination of FEX in pharmaceutical formulations.     

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   

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.