On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n

In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers. As an application, we use the method for finding the number of solutions of a Diophantine inequality

Transitions through Critical Temperatures in Nematic Liquid Crystals

We obtain ‘dynamic’ estimates for critical nematic liquid crystal (LC) temperatures with a slowly varying temperature-dependent control variable. We focus on two critical temperatures : the supercooling temperature below which the isotropic phase loses stability and the superheating temperature above which the ordered nematic states do not exist. In contrast to the static problem, the isotropic phase exhibits a memory effect below the supercooling temperature. This delayed loss of stability is independent of the rate of change of temperature and depends purely on the initial value of the temperature

Cricket bowling: A two-segment Lagrangian model

In this study, a Lagrangian forward solution of the bowling arm in cricket is made using a two-segment rigid body model, coupled with projectile equations for the free flight of the ball. For given initial arm positions and constant joint torques, the equations are solved numerically to determine the ball speed and arm angle at release so that the ball can land on a predetermined position on the pitch. The model was driven with kinematic data from video obtained from an elite bowler. The model can be analysed in order to study the biomechanics of the bowling arm as well as to quantify the effects of changing input parameters on the trajectory and speed of the ball

Space shuttle external tank performance improvements: The challenge

The external tank (ET) has been actively involved in performance improvements since the inception of the space shuttle program, primarily by weight savings. Weight savings were realized on the first block of flight articles (standard weight tank). With a need for further performance improvements, the ET Program Office was requested to develop a program to reduce tank weight an additional 6000 lb and schedule delivery of the first lightweight ET (LWT) for June 1982. The weight savings program was accomplished by: (1) a unique approach to use of factors of safety; (2) design optimization; and (3) redesign of structures with large margins of safety which resulted in an actual weight savings of 7294 lb. Additional studies have identified further weight savings which are to be implemented at appropriate times in production flow. Examples are an improved thermal protection system for the LH2 tank aft dome and reduction of slosh baffles in the LO2 tank based on flight data. All performance improvements were compared and selected based on non-recurring and recurring cost and technical risk

Computational fluid dynamics: Transition to design applications

The development of aerospace vehicles, over the years, was an evolutionary process in which engineering progress in the aerospace community was based, generally, on prior experience and data bases obtained through wind tunnel and flight testing. Advances in the fundamental understanding of flow physics, wind tunnel and flight test capability, and mathematical insights into the governing flow equations were translated into improved air vehicle design. The modern day field of Computational Fluid Dynamics (CFD) is a continuation of the growth in analytical capability and the digital mathematics needed to solve the more rigorous form of the flow equations. Some of the technical and managerial challenges that result from rapidly developing CFD capabilites, some of the steps being taken by the Fort Worth Division of General Dynamics to meet these challenges, and some of the specific areas of application for high performance air vehicles are presented

Thanks, but no thanks: women's avoidance of help-seeking in the context of a dependency-related stereotype

The stereotype that women are dependent on men is a commonly verbalized, potentially damaging aspect of benevolent sexism. We investigated how women may use behavioral disconfirmation of the personal applicability of the stereotype to negotiate such sexism. In an experiment (N = 86), we manipulated female college students’ awareness that women may be stereotyped by men as dependent. We then placed participants in a situation where they needed help. Women made aware of the dependency stereotype (compared to controls who were not) were less willing to seek help. They also displayed a stronger negative correlation between help-seeking and post help-seeking affect - such that the more help they sought, the worse they felt. We discuss the relevance of these findings for research concerning women’s help-seeking and their management of sexist stereotyping in everyday interaction. We also consider the implications of our results for those working in domains such as healthcare, teaching and counseling, where interaction with individuals in need and requiring help is common

Photon counting compressive depth mapping

We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 x 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 x 32 pixel real-time video for three-dimensional object tracking at 14 frames-per-second.Comment: 16 pages, 8 figure