Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.

Variability Modelling for Model-Driven Development of Software Product Lines

Abstract: Model-driven development of software-intensive systems aims at designing systems by stepwise model refine- ment. In order to create software product lines by model-driven development, product variability has to be represented on every modelling level and preserved under model refinement. In this paper, we propose ∆-modelling as an generally applicable variability modelling concept that is orthogonal to model refinement. Products on each modelling level are represented by a core model and a set of ∆-models specifying changes to the core to incorporate product features. Core and ∆-models can be refined independently to obtain a more detailed model of the product line. Based on a formalization of ∆-modelling, we establish conditions that model refinement and model configuration commute resulting in an incremental model- driven development process.

Analysis of the asymmetric shortest queue problem

Abstract: In this paper we study a system consisting of two parallel servers with different service rates. Jobs arrive according to a Poisson stream and generate an exponentially distributed workload. On arrival a job joins the shortest queue and in case both queues have equal lengths, he joins the first queue with probability q and the second one with probability 1- q, where q is an arbitrary number between 0 and 1. In a previous paper we showed for the symmetric problem, that is for equal service rates and q = ½, that the equilibrium distribution of the lengths of the two queues can be exactly represented by an infinite sum of product form solutions by using an elementary compensation procedure. The main purpose of the present paper is to prove a similar product form result for the asymmetric problem by using a generalization of the compensation procedure. Furthermore, it is shown that the product form representation leads to a numerically efficient algorithm. Essentially, the method exploits the convergence properties of the series of product forms. Because of the fast convergence an efficient method is obtained with upper and lower bounds for the exact solution. For states further away from the origin the convergence is faster. This aspect is also exploited in the paper. Keywords: bounds, difference equation, product form, queues in parallel, stationary queue length distribution, shortest queue problem.

Method and apparatus for storing and selectively retrieving and delivering product data based on embedded expert judgements

Abstract: An improved apparatus and method of storing and selectively retrieving and delivering product data is disclosed. Product data files, product lists, product directories and allowable customer data entry sets are stored in a data storage device. The customer is asked to specify one or more criteria relating to a product need or desire and one or more allowable customer data entry sets are selected that best correspond to these criteria. The customer data entry sets are connected to product directories and the directories are in turn connected to product lists that reference the data files of products having anticipated common uses. The product directories correspond to connected customer data entry sets with different degrees of specificity and the product lists correspond to connected product directories with different degrees of specificity or applicability. The apparatus is thus able to retrieve and display a variety of products in response to any given customer input and is also able to respond to many different kinds of customer entered criteria.

Discrete C*-coactions and C*-algebraic bundles

Abstract: Discrete C*-coactions are shown to be equivalent to discrete C* -algebraic bundles. Simplicity, primeness, liminality, postliminality, and nuclearity are related to the fixed point algebra and the cocrossed product. Ergodic, and more generally homogeneous, C*-coactions are characterized.

Product engineering of dispersed systems

Abstract: Product engineering is the design of products with desired properties using the methods of process engineering. To reduce the number of process parameters, necessary to obtain the desired properties, a characteristic feature of the respective product is helpful. For a dispersed system this characteristic feature is its complex structure on a micro-scale. This micro-structure is the link between the process and the properties of the final product. The principles of product engineering of dispersed systems are explained and demonstrated by means of different examples: Though there are limits to this concept, certain properties of dispersed systems can be obtained by determining and applying property and process functions.