Iterative methods for a fourth order boundary value problem

We consider a fourth order nonlinear ordinary differential equation together with two-point boundary conditions and provide a-priori error estimates on the length of the interval (b?a) so that the Picard's iterative method, the approximate Picard's iterative method and the quasilinear iterative method convergence to the solution of the problem.     

The preferred mode of cycloreversion of some 1,3,4-substituted azetidin-2-ones upon electron impact

The mass spectra of some 1,3,4-substituted azetidin-2-ones are measured. Fragmentation pathways are confirmed by use of both high-resolution and mass-analysed ion kinetic energy. They are consistent with the possible [2 + 2]- cycloadditions through which the azetidin-2-ones may be synthesized. More attention has to be paid to further fragmentations of the main fragments in assessing the preferred fragmentation mode. Influence of side-chain substituents is discussed.     

A renewal theorem and its applications to some sequential procedures

Probability Theory and Related Fields - A renewal theorem of the elementary type for some stopping times which arise from some statistical estimation problems has been established. It is applied to...     

Photoionization and photoelectron angular distribution for H2

Photoionization of H₂(¹Σ_g⁺) in a vibrational υ″ and rotational N″ state into H₂⁺(²Σ_g⁺) in a vibrational υ′ and rotational N′ state is studied theoretically. The differential cross section, after summing over the final states, is expressed in the well-known simple form of $\text{(}\text{σ}{}_{\mathrm{T}}\text{4π}\text{)[1 + βP}{}_2\text{(}\text{cos}\text{θ)]}$. Parallel expressions are obtained for H₂⁺ in a specific υ′ state (in terms of σ(υ′) and β(υ′)) and for H₂⁺ in a rotational fine level υ′N′ (in terms of σ(υ′N′) and β(υ′N′)). Asymmetry parameters β, β(υ′) and β υ′N′), which are expressed in terms of Racah and Clebsch-Gordan coefficients and electronic transition moments, can be reduced approximately to 2 lineary polarized light and to -1 for unpolarized light. Using single-center electronic wave functions and including partial eaves l = 1, 3, and 5, σ(υ′) and β(υ′) are computed as a function of υ′ at 584 Å. The computed σ(υ′) divided by the Frank-Condon overlap, in agreement with experimental results, increases monotonically with υ′; σ_T and β are computed in the incident photon energy range of 600–4000 Å and the results compare favorably with previous calculations.     

A class of singularly perturbed,nonlinear, fixed-endpoint control problems

Singular perturbation techniques are applied to a class of nonlinear, fixed-endpoint control problems to decompose the full-order problem into three lower-order problems, namely, the reduced problem and the left and right boundary-layer problems. The boundary-layer problems are linear-quadratic and, contrary to previous singular perturbation works, the reduced problem has a simple formulation. The solutions of these lower-order problems are combined to yield an approximate solution to the full nonlinear problem. Based on the properties of the lower-order problems, the full problem is shown to possess an asymptotic series solution.This work was supported in part by the National Science Foundation under Grant No. ENG-47-20091 and in part by the US Air Force under Grant No. AFOSR-73-2570.The author acknowledges the helpful suggestions of Professor P. V. Kokotovic, University of Illinois, Urbana, Illinois.     

Dual function catalysts. Dehydrogenation and asymmetric intramolecular Diels-Alder cycloaddition of N-hydroxy formate esters and hydroxamic acids: evidence for a ruthenium-acylnitroso intermediate

The chiral ruthenium salen complex, 13b, functions as an efficient catalyst for the sequential oxidation and asymmetric Diels-Alder cycloaddition of hydroxamic acids and N-hydroxy formate esters. This result provides evidence for the formation of a ruthenium-nitroso formate (acyl nitroso) intermediate. The Diels-Alder precursors are prepared from simple building blocks, and the cycloadducts, bridged oxazinolactams, can serve as useful intermediates in organic synthesis.