Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are respectively based on a formula of Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott-Samelson resolution. These constructions give distinct answers to a question of Deodhar.Comment: 43 page

Effect of Firing Conditions & Release Height on Terminal Performance of Submunitions and Conditions for Optimum Height of Release

Submunitions should exhibit optimum terminal performance at target end when released from certain pre-determined height. Selection of an optimum height of release of the submunitions depends on the terminal parameters like forward throw, remaining velocity, impact angle and flight time. In this paper, the effects of initial firing conditions and height of release on terminal performance of submunitions discussed in detail. For different height of release, the relation between range and forward throw is also established & validated for a number of firing altitude and rocket configurations

Dispersion sensitivity analysis & consistency improvement of APFSDS

The purpose of this study is to investigate and quantify some possible sources of dispersion of 120 mm APFSDS tank ammunition both experimentally and numerically. This paper aims to point out the most influential source during In-Bore Balloting Motion phase as well as in External Ballistics phase of the ammunition and quantifies its effect on dispersion. Data obtained from flight trials is critically analysed and parameters affecting dispersion such as initial yaw/pitch rates, yaw/pitch dampening, plane start angle, launch spin, clearance, centre of gravity shift, dynamic imbalance angle, cross wind, etc. are observed and, later on, studied in detail by extensive External Ballistics Monte Carlo (EBMC) simulation and Six Degree of Freedom (6-DOF) trajectory analysis. In Bore Balloting Motion simulation shows that reduction in residual spin by about 5% results in drastic 56% reduction in first maximum yaw. A correlation between first maximum yaw and residual spin is observed. Results of data analysis are used in design modification for existing ammunition. Number of designs are evaluated numerically before freezing five designs for further soundings. These designs are critically assessed in terms of their comparative performance during In-bore travel & external ballistics phase. Results are validated by free flight trials for the finalised design