Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group.Comment: 26 pages; corrected misprints; simplified Definition 2; more references adde

Le mini-élevage et la faune: 1983-2002

Minilivestock and Fauna: 1983-2002. The author makes a synthesis on the trend observed through the first twenty volumes of Tropicultura regarding papers on minilivestock and wild fauna. Specialized journals produce indeed more articles on controlled breeding of rodents, guinea pigs for meat, reptiles, insects, manure worms, crocodiles, antelopes or other game species. Giant snails, cricetomas and frogs have been dealt with most often in this periodical. Minilivestock can play an important role for biodiversity preservation and against poaching

Duality and interval analysis over idempotent semirings

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose of this paper is to consider a dual product, denoted $\odot$, and the dual residuation of matrices, in order to solve the following inequality $A \otimes X \preceq X \preceq B \odot X$. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals

Model Decomposition of Timed Event Graphs under Partial Synchronization in Dioids (I)

Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t1,t2 can only fire if both transitions are simultaneously enabled, PS of transition t1 by transition t2 means that t1 can fire only when transition t2 fires, but t1 does not influence the firing of t2. Under some assumptions, we can show that the dynamic behavior of a TEG under PS can be decomposed into a time-variant and a time-invariant part. The time-invariant part can be interpreted as a standard TEG. Moreover, it is shown that the tools introduced for standard TEGs can be used to analyze the overall system

The Sol of New Orleans: an Undergraduate Design Experience

This paper presents the incorporation of the design, construction, and testing of a solar-powered car into the undergraduate curriculum of the Electrical Engineering Department of the University of New Orleans. All work on the vehicle is entirely performed by students who earn design credits in our Senior EE Design Project and/or Special Problems in EE courses

Optimal Control of a Class of Timed Discrete Event Systems with Shared Resources, An Approach Based on the Hadamard Product of Series in Dioids

The topic of this paper is modeling and control of timed discrete event systems in a dioid framework if systems operate under the restriction of shared resources. The behavior of such systems can be elegantly modeled using the Hadamard product of series in dioids. Using residuation of the Hadamard product, it is possible to compute optimal control, where optimality is in the sense of a lexicographical order reflecting the chosen prioritization of subsystems. The paper concludes with an example, illustrating the efficiency of the proposed method

Max-plus-linear Systems for Manufacturing Systems: Modeling and Control

In this chapter, the dynamics of manufacturing systems is characterized through the occurrence of events such as parts entering or leaving machines. Furthermore, we assume that the relations between events are expressed by synchronizations (i.e., conditions of the form: for all k greater than or equal to l, occurrence k of event e2 is at least t units of time after occurrence k-l of event e1). Note that this assumption often holds when the considered manufacturing system is functioning under a predefined schedule. First, we discuss the modeling of such systems by linear statespace models in the (max;+)-algebra (due to this property, such systems are often called (max;+)-linear systems). Second, standard open-loop and closed-loop control structures for (max;+)-linear systems are recalled. These control structures lead to a trade-off between the rapidity of systems and their internal buffer sizes. Some techniques to influence this trade-off are presented