Flow through a plateau border of cellular foam

Experimentally measured average velocities through plateau borders of stationary cellular foam, when compared with those calculated with the assumption of rigid Plateau Border walls, show that the assumption of rigid walls severely underestimates the velocities. An analysis of the situation wherein plateau border walls have velocities, as decided by the surface viscosity of the system, is presented here. The plateau border is idealized as a pipe of equilateral triangular cross-section with vertices of the triangle having zero velocity. The pertinent form of Navier-Stoke's equations with inhomogeneous boundary conditions and its solution through a procedure of successive approximations is presented in dimensionless form. The solution reduces to the known solution of slow steady flow through a triangular pipe, when surface viscosity is infinite. Results indicate that the assumption of rigid plateau border walls is valid only when value of the inverse of dimensionless surface viscosity is less than 0.044. Beyond that the assumption severely underestimates the flow and the effect of nonrigidity of the wall must be considered.

Border basis detection is NP-complete

Border basis detection (BBD) is described as follows: given a set of generators of an ideal, decide whether that set of generators is a border basis of the ideal with respect to some order ideal. The motivation for this problem comes from a similar problem related to Grobner bases termed as Grobner basis detection (GBD) which was proposed by Gritzmann and Sturmfels (1993). GBD was shown to be NP-hard by Sturmfels and Wiegelmann (1996). In this paper, we investigate the computational complexity of BBD and show that it is NP-complete.

Recent freshwater Ostracoda and Bivalvia from Indo-Nepal border (Tethys Himalaya): Ecological implications

We report for the first time Recent ostracods and bivalves from Central Tethys Himalaya, collected from Changru village, which is situated in the Tinker valley of northwestern Nepal near the Indo-Nepal border. The specimens were collected from the surface sediments of a small pond, shaped by a small tributary of the glacier fed Tinker River. The ostracod species belonging to the families Ilyocyprididae, Cyprididae and Candonidae and one bivalve (Pisidium sp., Family Pisidiidae) have been identified. Psychrodromus olivaccus and Potamocypris villosa are being reported for the first time from India and Nepal. Several broken and unidentifiable gyrogonites of charophyta were also recovered. The ostracod sample, as a whole, points to a shallow freshwater lake environment influenced by slowly running carbonate rich waters under cool temperatures, low mineralization and sparse vegetation. This is in accordance with the occurrence of Pisidium, which is commonly associated with ostracods in the freshwater lakes and streams. The ostracod fauna shows affinity with the fossil and extant forms recovered from the Higher and Tethys Himalaya of NW India. This opens a new opportunity for studying ostracods in the Indian Central Himalaya - a region which otherwise has been ignored until now.