Product (mathematics)

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

Sequential quantum measurements

Abstract: A quantum effect is an operator A on a complex Hilbert space H that satisfies 0⩽A⩽I. We denote the set of quantum effects by E(H). The set of self-adjoint projection operators on H corresponds to sharp effects and is denoted by P(H). We define the sequential product of A,B∈E(H) by A∘B=A1/2BA1/2. The main purpose of this article is to study some of the algebraic properties of the sequential product. Many of our results show that algebraic conditions on A∘B imply that A and B commute for the usual operator product. For example, if A∘B satisfies certain distributive or associative laws, then AB=BA. Moreover, if A∘B∈P(H), then AB=BA and A∘B=B or B∘A=B if and only if AB=BA=B. A natural definition of stochastic independence is introduced and briefly studied.

Product structures on four dimensional solvable lie algebras

Abstract: It is the aim of this work to study product structures on four dimensional solvable Lie algebras. We determine all possible paracomplex structures and consider the case when one of the subalgebras is an ideal. These results are applied to the case of Manin triples and complex product structures. We also analyze the three dimensional subalgebras.

Multiple-view feature modelling for integral product development

Abstract: To allow a designer to focus on the information that is relevant for a particular product development phase, is an important aspect of integral product development. Unlike current modelling systems, multiple-view feature modelling can adequately support this, by providing an own view on a product for each phase. Each view contains a feature model of the product specific for the corresponding phase. An approach to multiple-view feature modelling is presented that supports conceptual design, assembly design, part detail design and part manufacturing planning. It does not only provide views with form features to model single parts, as previous approaches to multiple-view feature modelling did, but also a view with conceptual features, to model the product configuration with functional components and interfaces between these components, and a view with assembly features, to model the connections between components. The general concept of this multiple-view feature modelling approach, the functionality of the four views, and the way the views are kept consistent, are described.

Abstract delta modeling

Abstract: Delta modeling is an approach to facilitate automated product derivation for software product lines. It is based on a set of deltas specifying modifications that are incrementally applied to a core product. The applicability of deltas depends on feature-dependent conditions. This paper presents abstract delta modeling, which explores delta modeling from an abstract, algebraic perspective.Compared to previous work, we take a more flexible approach with respect to conflicts between modifications and introduce the notion of conflict-resolving deltas. We present conditions on the structure of deltas to ensure unambiguous product generation.