Star formation triggering mechanisms are reviewed, including the direct compression of clouds and globules, the compression and collapse of molecular clouds at the edges of HII regions and supernovae, the expansion and collapse of giant rings and shells in galaxy disks, and the collision and collapse between two clouds. Collapse criteria are given. A comprehensive tabulation of regions where these four types of triggering have been found suggests that dynamical processes sustain and amplify a high fraction of all star formation that begins spontaneously in normal galaxy disks.

Finite sample size corrections to the reparametrization-invariant solution of the inverse problem of probability are computed, and shown to converge uniformly to the correct distribution.

One of the few remaining astronomical bands (factor of $\sim$10 in energy range) still without an all-sky imaging survey is the hard x-ray band (10-600 keV). This is in spite of sensitive imaging all-sky surveys already conducted at soft x-ray energies (0.2-2 keV; ROSAT) and soft/hard $\gamma$-ray ($\sim$750 keV - 10 GeV; COMPTEL/EGRET) energies and imminent for medium x-ray energies (2- 10 keV; ABRIXAS). A Hard x-ray imaging survey conducted with wide-field coded aperture telescopes allows both high sensitivity (and spatial/spectral resolution) and broad temporal coverage. We derive a generalized survey sensitivity/temporal parameter, Q, and compare previous and planned hard x-ray surveys with the proposed EXIST mission. Key scientific objectives that could be addressed with the enhanced capability of EXIST are outlined.

The hard x-ray (10-600 keV) sky is inherently time variable and yet has neither been surveyed nor monitored with a sensitive imaging telescope. The Energetic X-ray Imaging Survey Telescope (EXIST) is a mission concept, proposed for MIDEX, which would conduct the first imaging all-sky hard x-ray survey as well as provide a sensitive all sky monitor. With $\sim 60%$ sky coverage each orbit, and full sky coverage each 50 days, hard x-ray studies of gamma-ray bursts, AGN, galactic transients, x-ray binaries and accretion-powered pulsars can be conducted over a wide range of timescales. We summarize the scientific objectives of EXIST for both the survey and monitoring objectives. We describe the mission concept and the instrumentation approach, which would incorporate a large area array of Cd-Zn-Te (CZT) detectors, as well as some of our ongoing development of CZT array detectors.

The progressive mixing and contamination of interstellar gas by supernovae and other processes following the passage of a spiral density wave is reviewed, with an emphasis on the Solar neighborhood. Regions of star formation should begin their lives with an inhomogeneous mixture of abundances as a result of their chaotic and large-scale formation processes. These inhomogeneities should continue to increase during several generations of star formation until the gas enters the interarm region. Then cloud dispersal by large interarm tidal forces, high rates of shear, and internal star formation should all lead to cloud-to-cloud mixing, while increased ionization, heating, and evaporation should lead to mixing on the atomic level. Gradients in the dispersion of elemental abundances are expected for galaxy disks.

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions $f(u)$ for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be derived.

Although Lorentz symmetry has been tested at low energy with extremely good accuracy, its validity at very high energy is much less well established. If Lorentz symmetry violation (LSV) is energy-dependent (e.g. $\propto E^2$), it can be of order 1 at Planck scale and undetectable at GeV scale or below. Similarly, superluminal particles with positive mass and energy (superbradyons) can exist and be the ultimate building blocks of matter. We discuss a few cosmological consequences of such a scenario, as well as possible experimental tests.

Several payloads for hard X-ray (20-600 keV) imaging with coded aperture telescopes have been developed for balloon flight observations of cosmic x-ray sources. We briefly review the characteristics of these, particularly the EXITE2 system. The recent NASA program to develop an extended long duration (100d) balloon flight capability employing super-pressure balloons would allow a qualitatively new hard x-ray imaging experiment: the Energetic X-ray Imaging Survey Telescope-Long Integration Time Experiment (EXIST-LITE). The longer continuous viewing times (per source) available from an LDB platform than from low earth orbit would enable both surveys and objectives complementary to the EXIST mission proposed for a MIDEX satellite. We summarize the scientific objectives of EXIST-LITE, a possible instrumentation approach incorporating a large area array of Cd-Zn-Te (CZT) detectors, and our program for the development and balloon flight testing of relatively thick (5mm) CZT detector arrays.

Virbhadra and Parikh studied the energy distribution associated with stringy charged black hole in Einstein's prescription. We study the same using Tolman's energy-momentum complex and get the same result as obtained by Virbhadra and Parikh. The entire energy is confined inside the black hole.

We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstein's equations), we set to zero the coefficients of derivatives that do not appear in Einstein's equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein's equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations.