Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in object-oriented (OO) programming, recursive hierarchies of object types with virtual methods play a central role for the same reason. There is a semantical correspondence ...

In this paper, we study the H∞ optimal filtering for multiparameter singularly perturbed system (MSPS). In order to obtain the solution, we must solve the multiparameter algebraic Riccati equations (MARE) with indefinite sign quadratic term. First, the existence of a unique and bounded solution of such MARE is newly proven. The main results in this paper are to propose a new recursive algorithm...

Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in object-oriented (OO) programming, recursive hierarchies of object types with virtual methods play a central role for the same reason. There is a semantical correspondence ...

Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

This paper presents a novel computationally efficient Closed Loop Dual-Mode Nonlinear Model Predictive Control scheme that uses closed loop models for condensing-based multiple-shooting frameworks which result in numerically robust optimisations. The proposed approach Time-Varying gains obtained from solving the Discrete Algebraic Ricatti Equation to embed feedback around trajectory, and proves...

Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This is relevant for both communities of computer scientists and mathematical analysts, particularly the latter who do not understand (and/or like) the language ...

How can we enumerate the inhabitants of an algebraic datatype? This paper explores a datatype generic solution that works for all regular types and indexed families . The enumerators presented here are provably both complete unique —they will eventually produce every value exactly once—and fair avoid bias when composing enumerators. Finally, these memoise previously enumerated values whenever p...