Jacobian

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function~: R “+ Rm. ADIFOR(Automatic Differentiation In FORtran) is a source transformation tool that accepts Fortran 77 code for ...

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g and h. In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

In this article, we study lower and upper triangular factorizations of the complex Wishart matrix. Further, using these factorizations, we obtain several expected values of scalar and matrix valued functions of the complex Wishart matrix. We also generalize Muirhead’s identity for the complex case which gives a number of interesting special cases.

Very little is known about the existence of curves, and families of curves, whose Jacobians are acted on by large rings of endomorphisms. In this paper, we show the existence of curves X with an injection K↪Hom(Jac(X), Jac(X))⊗ , where K is a subfield of even index at most 10 in a primitive cyclotomic field (ζp), or a subfield of index 2 in (ζpq) or (ζpα). This result generalizes previous work of Brumer, Mestre, and Tautz, Top, and Verberkmoes. Our curves are constructed as branched covers of the projective line, and the endomorphisms arise as quotients of double coset algebras of the Galois groups of these coverings. In certain cases, we show the existence of continuous families of Jacobians admitting the desired endomorphism algebras. At the end, we raise some questions about upper bounds for endomorphism algebras of the type described here and ask about a “non-Galois version of Hurwitz's theorem.”

ABSRACT Many of the robotic grasping researches have been focusing on stationary objects. And for dynamic moving objects, researchers have been using real time captured images to locate objects dynamically. However, this approach of controlling the grasping process is quite costly, implying a lot of resources and image processing.Therefore, it is indispensable to seek other method of simpler handling… In this paper, we are going to detail the requirements to manipulate a humanoid robot arm with 7 degree-of-freedom to grasp and handle any moving objects in the 3-D environment in presence or not of obstacles and without using the cameras. We use the OpenRAVE simulation environment, as well as, a robot arm instrumented with the Barrett hand. We also describe a randomized planning algorithm capable of planning. This algorithm is an extent of RRT-JT that combines exploration, using a Rapidly-exploring Random Tree, with exploitation, using Jacobian-based gradient descent, to instruct a 7-DoF WAM robotic arm, in order to grasp a moving target, while avoiding possible encountered obstacles. We present a simulation of a scenario that starts with tracking a moving mug then grasping it and finally placing the mug in a determined position, assuring a maximum rate of success in a reasonable time.

The detailed modelling of heterogeneous catalytic systems is challenging due to the unknown nature of new catalytic materials as well as the often required transient nature of the resulting models. Thus, this thesis deals with the methodologies involved in the kinetic modelling of heterogeneous catalysis and in particular NOx reduction systems. The methods presented increase the understanding of the interplay between model parameters and also decrease the number of necessary laboratory experiments. The effect of more efficient parameter estimation methods should result in faster model development which is required in any process development but especially for catalytic emission control. In the first paper, injection parameters for an engine rig with a NOx Storage and Reduction (NSR) system were optimised using different experimental designs at different load points. The optimised settings were used as a map for a control strategy complying with a European Transient Cycle (ETC). In t...

This paper analyzes the stability of a general RLC circuit with ideal thyristors or diodes and periodic sources. Applications include high power thyristor controlled reactor and bridge rectifier circuits. The periodic steady states of the circuit are analyzed using a Poincare map and transversality conditions are given to guarantee the smoothness of the Poincare map. A simple and exact formula