An Integro-Differential Structure for Dirac Distributions

We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems handling such objects. In particular, we show that the Green's function of regular boundary problems (for linear ordinary differential equations) can be expressed naturally in the new setting and that it is characterized by the corresponding distributional differential equation known from analysis.Comment: 38 page

Free integro-differential algebras and Groebner-Shirshov bases

The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations. In both cases, free objects are crucial for analyzing the underlying algebraic structures, e.g. of the (matrix) functions. In this paper we apply the method of Groebner-Shirshov bases to construct the free (noncommutative) integro-differential algebra on a set. The construction is from the free Rota-Baxter algebra on the free differential algebra on the set modulo the differential Rota-Baxter ideal generated by the noncommutative integration by parts formula. In order to obtain a canonical basis for this quotient, we first reduce to the case when the set is finite. Then in order to obtain the monomial order needed for the Composition-Diamond Lemma, we consider the free Rota-Baxter algebra on the truncated free differential algebra. A Composition-Diamond Lemma is proved in this context, and a Groebner-Shirshov basis is found for the corresponding differential Rota-Baxter ideal

Aggregation of Hospital Business Processes

There are estimates that up to 30% of hospital costs are due to inefficiently coordinated hospital processes. As a result many hospitals have tried to model and to reengineer their business processes. These efforts have very often been abandoned, because the normally constructed total models of hospital processes could hardly cope with the rapid technological and medical progress as well as with changing staff. We discuss approaches for a qualitative and quantitative process modularization which improve the understanding of processes and enables better planned simulations. Various methods are discussed which allow a qualitative modularization on the basis of a disaggregated process graph. To cope with this modularization numerically simple semi-stochastic formulas are developed for the calculation of expected values and variances of cycle times and costs from micro-data up to the modular level. Thus a qualitative as well as quantitative discussion of hospital business processes on the modular level become possible.OR in health care service, graph theory, business process reengineering, stochastic processes, simulation

Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Groebner Bases

We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras. The algebraic treatment of boundary problems brings up two new algebraic structures whose symbolic representation and computational realization is based on canonical forms in certain commutative and noncommutative polynomial domains. The first of these, the ring of integro-differential operators, is used for both stating and solving linear boundary problems. The other structure, called integro-differential polynomials, is the key tool for describing extensions of integrodifferential algebras. We use the canonical simplifier for integro-differential polynomials for generating an automated proof establishing a canonical simplifier for integro-differential operators. Our approach is fully implemented in the THEOREMA system; some code fragments and sample computations are included

Aggregation of Hospital Business Processes

There are estimates that up to 30% of hospital costs are due to inefficiently coordinated hospital processes. As a result many hospitals have tried to model and to reengineer their business processes. These efforts have very often been abandoned, because the normally constructed total models of hospital processes could hardly cope with the rapid technological and medical progress as well as with changing staff. We discuss approaches for a qualitative and quantitative process modularization which improve the understanding of processes and enables better planned simulations. Various methods are discussed which allow a qualitative modularization on the basis of a disaggregated process graph. To cope with this modularization numerically simple semi-stochastic formulas are developed for the calculation of expected values and variances of cycle times and costs from micro-data up to the modular level. Thus a qualitative as well as quantitative discussion of hospital business processes on the modular level become possible

Inhibiting Factors for Adopting Enterprise Systems in Networks of Small and Medium-Sized Enterprises - An Exploratory Case Study

Effective use of an enterprise system may result in productivity and quality improvements, cost reductions and a better resource management but also bears non-negligible risks. Since enterprise systems usually exhibit a proliferating complexity, many small and medium-sized enterprises fail to pass this hurdle. Therefore, the imperative of this research is to develop an understanding of what inhibits or drives the adoption of enterprise systems in networks of small and medium-sized enterprises. We use an exploratory case study to propose first explanations of the variables and factors that affect the adoption of an enterprise system for such a network