algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

The χ language is a hybrid language for modeling, simulation and verification. As a result of the recently completed formal semantics, the language now consists of a number of orthogonal operators that operate on all process terms, including differential algebraic equations. The same χ model can be used for simulation and verification. Verification is possible after a straightforward syntactica...

If a model structure is not identifiable, then it is not possible to uniquely identify its parameters from measured data. This contribution describes how solvers for differential-algebraic equations (DAE) can be used to examine if a model structure is locally identifiable. The procedure can be applied to both linear and nonlinear systems. If a model structure is not identifiable, it is also pos...

1

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the meth...

Phasor measurement units (PMUs) have become instrumental in modern power systems for enabling real time, wide-area monitoring and control. Accordingly, many studies investigated efficient robust dynamic state estimation (DSE) methods order to accurately compute the states of generation units. Nonetheless, most them forego dynamic-algebraic nature networks only consider their nonlinear represent...

In the last decade, researchers in numerical simulation have worked on defining standards for specifying physical models at the mathematical level of abstraction of Differential Algebraic Equations, or DAEs one can in particular mention the Modelica initiative. Today, tools for performing simulation, i.e. checking, interpreting or compiling mathematical models into simulation programs, are bein...