In this lecture we learn to solve nonhomogeneous equations of the form ay′′ + by′ + cy = g(t) using the “method of undetermined coefficients”. In previous lectures we learned to how to solve any equation of the form ay′′ + by′ + cy = 0. We will apply these techniques to help us solve the nonhomogeneous equation ay′′ + by′ + cy = g(t) by understanding the connection between solutions to homogene...

I came to Columbia in 1968 as an undergraduate in the engineering school. I didn’t know what I wanted to major in, and declared an interest in nuclear engineering, so that I could take as many physics courses as I wanted. But the summer after my freshman year I took a summer job in Washington D.C. at an Army lab for which I had qualified by taking a civil service exam. They had an OR group, and...

Article history: Received 1 April 2011 Received in revised form 21 June 2012 Accepted 12 August 2012 Available online 30 August 2012 Notwithstanding their many environmental, economic and social advantages, renewable energy technologies (RE) account for a small fraction of the world's primary energy supply. One possible cause for this limited diffusion is that private investments in the RE sect...

The cdebruted ri-we-Rdinson-ThraU (Canad. J. Math. 6 (1954) 316-324) hook-lengths formula, counting the foung tableaux of a specified shape, is given a shart bijective proof. This proof was obtained by translating the elegant Greene-Nijenhuis-Wilf proof (Adv. in Math. 31 (1979) f&l-109) into bijective language. 1 GjG&) satisfying qj <*+lj and ej C= Rj+l (whenever applicable) such that every int...

(a) (b) (c) (d) (e) (f) (g) (h) Figure 1. Endoscope calibration setup: (a) geometric calibration (b-d) images of 5 × 4 checker board used for geometric calibration. (e) photometric calibration. (f-g) images of Macbeth color chart used for photometric calibration. The orthopedic endoscope has a single camera and one or more point light sources equipped at the tip of the scope. For this work, we ...

Many insects have an innate propensity to approach conspicuous objects. We explore how such beacon aiming determines the shape of a wood ant's habitual route. We find that a single large black cylinder within an arena biases the route taken by ants as they run from a start position at one end of the arena to reach a feeder at the other. Ants learn a stable route with the first segment of their ...

We present a new curve skeleton model designed for surface modeling and processing. This skeleton is defined as the geometrical integration of a piecewise harmonic parameterization defined over a disk-cylinder surface decomposition. This decomposition is computed using a progressive Region Graph reduction based on both geometric and topological criteria which can be iteratively optimized to imp...

In the present paper, a complete literatures review of thermal barrier coating applications in diesel engines is performed to select a proper type and to find coating effects. The coating system has effects on the fuel consumption, the power and the combustion efficiency, pollution contents and the fatigue lifetime of engine components. Usually there are several beneficial influences by appl...