On the Exergy Content of an Isolated Body in Thermodynamic Disequilibrium

Exergy is a concept that is gaining an increasingly wider recognition as a proper measure for the actual energy resources consumed, when energy is used. Energy as such is indestructible, but exergy is not. As entropy is generated while energy is used, exergy is consumed. Exergy can be interpreted as the qualitative content of energy, or as energy in its highest quality. Therefore, there is an interest in investigating this concept from as many theoretical aspects as possible. In earlier papers the author has developed formulae for the exergy potential of a system of finitely extended objects, not necessarily having any environment. It was there shown that the classical formula for exergy obtains as one of the objects grows beyond all bounds thereby taking on the rôle as an environment. In this current paper formulae are derived for the exergy content of an isolated body in thermodynamic disequilibrium, viewed as a system of infinitely many objects each with infinitesimal extension and in microscopic equilibrium

On The Application of the Laplace Transform to Certain Economic Problems

During the last thirty years, the method of the Laplace transform has found an increasing number of applications in the fields of physics and technology. In this article the author points out the possibility of solving problems in the area of discounting with the aid of this method. Without any loss of general validity, it is shown that a discount factor can always be written in an exponential manner which implies that the present value of a cash-flow will obtain a very simple form in the Laplace terminology. This simplicity holds good for stochastic as well as for deterministic economic processes, and the results mentioned below should, therefore, be of immediate use when applied, e.g., to investment problems.

The time-averaged L4L solution - a condition for long-run stability applying MRP theory

MRP theory provides a theoretical background for multi-level, multi-stage production-inventory systems (material requirements planning in a general sense) together with their economic evaluation, in particular applying the net present value principle. The theory combines the use of input-output analysis and Laplace transforms, the former for capturing product structures, and the latter for incorporating timing, including time lags, lead times, and output delays. In this paper, we consider any production policy, when given any external demand as a vector-valued function of time. It is shown that in order for available inventory to be kept at finite levels at any time, the lot-for-lot (L4L) solution must be valid for the time averages of production and deliveries, irrespective of the policy followed. This analysis is carried out using properties the Laurent expansions of the transforms involved

Transient Aspects of MRP Theory - Abridged

MRP theory concerns production-inventory systems, in which produced items are made up of sets of sub-items, either produced or purchased (imported into the system) and required to be available a lead-time before the product is completed. The hierarchical dependence of relations between items is captured by the use of input matrices from Input-Output Analysis, the necessary advanced timing by applying the methodology of Laplace transforms, and the production-economic consequences by the net present value (NPV). This theory has been developed for about 40 years, but little attention has been given to transient aspects, i.e. when there happens to be an initial available inventory of items usable in future production. In this paper, we attempt to highlight the theoretical consequences from having a positive initial available inventory