Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r−2) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity...

To explore the conservation and cultivation of endangered alpine medicinal crops at comparatively lower altitudes, a study on variations in morphological parameters and energy exchange characteristics was conducted on five herbaceous medicinal crops from the alpines of Central Himalayas. Plants of same age were selected from the alpine medicinal crop nursery, Tungnath (3600 m), and were planted...

In this paper we show the existence of solutions to a nonlinear singular second order ordinary differential equation, u(t) = a t u(t) + λf(t, u(t), u(t)), subject to periodic boundary conditions, where a > 0 is a given constant, λ > 0 is a parameter, and the nonlinearity f(t, x, y) satisfies the local Carathéodory conditions on [0, T ] × R × R. Here, we study the case that a well-ordered pair o...