On Solving Some Trigonometric Series

This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a side effect. The new series are useful both for analysis, approximations and asymptotic studies.Comment: 12 pages, 2 figure

Construction of totally reflexive modules from an exact pair of zero divisors

Let A be a local ring which admits an exact pair x,y of zero divisors as defined by Henriques and Sega. Assuming that this pair is regular and that there exists a regular element on the A-module A/(x,y), we explicitly construct an infinite family of non-isomorphic indecomposable totally reflexive A-modules. In this setting, our construction provides an answer to a question raised by Christensen, Piepmeyer, Striuli, and Takahashi. Furthermore, we compute the module of homomorphisms between any two given modules from the infinite family mentioned above.Comment: 15 page

Legal Requirements for Admission to Public Schools

Advanced driver assistance systems for heavy duty vehicles, such as lookahead cruise and gearshift controllers, rely on high quality map data. Current digital maps do not offer the required level of road grade information. This contribution presents an algorithm for on-board road grade estimation based on fusion of GPS and vehicle sensor data with measurements from previous runs over the same road segment. An incremental update scheme is utilized to ensure that data storage requirements are independent of the number of measurement runs. Results of the implemented system based on six traversals of a known road with three different vehicles are presented.QC 20120216</p

Tube domains and restrictions of minimal representations

In this paper we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from $Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to $GL(n,\mathbb{C})$ respectively. We work with the realisations of the representation spaces as $L^2$-spaces on the boundary orbits of rank one of the corresponding cones, and give explicit integral operators that play the role of the intertwining operators for the decomposition. We prove inversion formulas for dense subspaces and use them to prove the Plancherel theorem for the respective decomposition. The Plancherel measure turns out to be absolutely continuous with respect to the Lebesgue measure in both cases

Model reduction of networked passive systems through clustering

In this paper, a model reduction procedure for a network of interconnected identical passive subsystems is presented. Here, rather than performing model reduction on the subsystems, adjacent subsystems are clustered, leading to a reduced-order networked system that allows for a convenient physical interpretation. The identification of the subsystems to be clustered is performed through controllability and observability analysis of an associated edge system and it is shown that the property of synchronization (i.e., the convergence of trajectories of the subsystems to each other) is preserved during reduction. The results are illustrated by means of an example.Comment: 7 pages, 2 figures; minor changes in the final version, as accepted for publication at the 13th European Control Conference, Strasbourg, Franc