We investigate some algorithms that produce Bernoulli, Euler and Genocchi polynomials. We also give closed formulas for Bernoulli, Euler and Genocchi polynomials in terms of weighted Stirling numbers of the second kind, which are extensions of known formulas for Bernoulli, Euler and Genocchi numbers involving Stirling numbers of the second kind.

A position and attitude tracking control law for autonomous underwater vehicles (AUVs) in 6 degrees of freedom (DOF) is derived. The 4-parameter unit quaternion (Euler parameters) is used in a singularity-free representation of attitude. Global convergence of the closed-loop system is proven. In addition several 3-parameter representations in terms of the Euler parameters are discussed with app...

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our im...

The Euler–Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler–Koszul homology with D-module direct images from the torus to the base space through orbits in the corresponding toric variety. Our approach generalizes a result by Gel’fand et al. [GKZ90, Thm. 4.6] and yields a simpler, more algebraic proof. In the ...

In this paper the traditional household Euler equations are estimated for singles and separately for couples. Using the Consumer Expenditure Survey, I reject the Euler equations of couples, but I cannot reject the Euler equations of singles. This result is rationalized using an intertemporal model with no intra-household commitment. Using this model it can be shown that an excess sensitivity te...