We present the first experimental observations of the dust acoustic wave where the wave was observed to propagate in the directions of gravity and magnetic field when these directions were not aligned. The experiments were conducted in the Magnetized Dusty Plasma eXperiment facility using a novel electrode system that allows for the angle between gravity and the magnetic field to be varied in a controlled way. This letter reports on measurements in an rf glow discharge argon plasma environment where the angle between direction of gravity and the magnetic field is 45$^{\circ }$. When there was no applied magnetic field, the wave was observed to propagate in the direction of gravity. However, as the magnetic field increased and the ions transitioned from flowing in the direction of gravity to the direction of the magnetic field, a second wave emerged and two distinct waves were observed to simultaneously propagate, one in the direction of gravity and one in the direction of the magnetic field. As the magnetic field was further increased, the wave that propagated in the direction of gravity was suppressed and the wave was only observed to propagate in the direction of the applied magnetic field. We also observe that the speed and the kinetic temperature of the dust for the mode that propagated in the direction of gravity decreased with increasing magnetic field while the speed and the kinetic temperature of the dust for the mode that propagated in the direction of the magnetic field increased with increasing magnetic field. These measurements suggest that an ion-dust streaming instability is at least partially responsible for the high temperatures that have previously been observed in dusty plasmas when the dust acoustic wave is present.

In this paper, we establish a new version of one-dimensional discrete improved Hardy’s inequality with shifts by introducing a shifting discrete Dirichlet’s Laplacian. We prove that the general discrete Hardy’s inequality as well as its variants in some special cases admit improvements. Further, it is proved that two-variable discrete $p$-Hardy inequality can also be improved via improved discrete $p$-Hardy inequality in one dimension. The result is also extended to the multivariable cases.

This paper reports results from the eighth of a series of road transect surveys of Gyps vultures conducted across northern, central, western, and north-eastern India since the early 1990s. Populations of the White-rumped Vulture Gyps bengalensis, Indian Vulture G. indicus, and Slender-billed Vulture G. tenuirostris declined rapidly, beginning in the mid-1990s. The principal cause of the declines was poisoning due to widespread veterinary use of the non-steroidal anti-inflammatory drug (NSAID) diclofenac on cattle. The results of the current survey suggest that, while populations of all three species of vulture remain at a low level with no signs of recovery, they appear to have been approximately stable since veterinary use of diclofenac was banned in the mid-2000s. Population trends in India, where the illegal use of diclofenac and legal use of other toxic NSAIDs continues, are compared with more positive trends in Nepal, where the veterinary use of toxic NSAIDs appears to have been reduced to a low level.