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Direct and indirect observations of interplanetary shock waves have been extended to the study of (i) the shock structure itself; (ii) the disturbed solar wind in its wake; (iii) additional discontinuities such as reverse shocks and pistons; and (iv) the shock's kinematic behavior. The last item - the trajectory - has benefited by the procedure (suggested by Pintér) of matching type II radio drift-inferred velocities with indirectly-inferred initial velocities found from at least two successive measurements in space. The significance of making type II observations at hectometric and kilometric wavelengths (as made, for example, by Slysh and Malitson, Feinberg and Stone) cannot be over-emphasized due to this technique's ability to make unambiguous solar terrestrial relationships. More direct and physically-meaningful observations, however, are still dependent upon in situ plasma and magnetic field measurements. Additional emphasis is presently being placed on numerical modeling of shock-induced disturbances in the solar wind as generated by both flares and stream-stream interactions. The former mechanism is emphasized in this review with several recommendations for further research: (a) further numerical modeling for shocks, starting when they are 'born' within relatively low-Alfvén speed coronal regions; (b) expanded synoptic studies by spacecraft at various heliocentric longitudes, radii, and (eventually) latitudes with coordinated diagnostics; and (c) extended patrol of natural probes, such as comets, augmented with theoretical studies of possible shock-induced mechanical and chemical effects. [ABSTRACT FROM AUTHOR]

The application of a Sartorius 4104 microbalance after Gast in vertical gradiometry was tested. A small mass of about 20 grams is suspended on thin fibers of different lengths Δℓ≤80 cm. From the weight difference of the small mass obtained at different levels along the plumb line the corresponding differences of gravity along the plumb line are inferred. The microbalance is mounted on a steal rack; measurements at constant low pressure (moderate vacuum) show the applicability of the balance as gravity difference sensor for field work. When environmental effects are further reduced (i,e, temperature is kept constant within ±0.1°C; pressure is controlled within 0.1 Torr etc.) the resolution of the balance can be fully exploited so a relative accuracy of ±10 should be feasible and for laboratory experiments should be of the order of a few parts in ±10. Vertical gravity gradients as observed on an improved moving platform with a LaCoste model G gravimeter are discussed. New possibilities of microgravimetry are pointed out. High precision observations and establishment of a system in an area of tectonic interest for detecting secular gravity changes are described. [ABSTRACT FROM AUTHOR]

This paper establishes quantitative bounds for the variation of an isolated local minimizer for a general nonlinear program under perturbations in the objective function and constraints. These bounds are then applied to establish rates of convergence for a class of recursive nonlinear-programming algorithms. [ABSTRACT FROM AUTHOR]

In the nonoscillation theory of ordinary differential equations the asymptotic behaviour of the solutions has often been described by exhibiting asymptotic expansions for these solutions. A fundamental illustration of this technique may be found in Hille [6] wherein the linearly independent solutions of a second order homogeneous differential equation were described by single termed asymptotic expansions. For the dominant solution, this result was successively extended by Waltman in [8] for a second order equation and in [9] for an nth order equation. A further generalization of these results appears in [3] where a complete nth order nonhomogeneous nonlinear differential equation was considered; again, asymptotic representations were given to describe the behaviour of the solutions of the differential equation. Moore and Nehari [7], Wong [10], [11], and Hale and Onuchic [2], also use asymptotic representations in discussing the behaviour of the solutions of certain differential equations. All of the above results are essentially perturbation problems with the unperturbed linear differential equation having the form y(n) = h(t) for some n and h(t). [ABSTRACT FROM PUBLISHER]