China
Africa
Explore chapters and articles related to this topic
Inference and Access Control for Big Data
Published in Bhavani Thuraisngham, Murat Kantarcioglu, Latifur Khan, Secure Data Science, 2022
Bhavani Thuraisngham, Murat Kantarcioglu, Latifur Khan
Graph rewriting came out of logic and database theory where graphs are treated as database instances, and rewriting operations as a mechanism for defining queries and views. Popular graph rewriting approaches include double-pushout approach, single-pushout approach and algebraic approach [EHRI1991]. The approach we describe is similar to the one for single-pushout approach. A graph rewriting system consists of a set of rewrite rules of the form p:L→R, with L being a graph pattern (or left hand side) and R being the replacement graph (or right hand side of the rule). A graph rewrite rule is applied to the original graph by searching for an occurrence of the pattern graph and replacing the found occurrence by the existence of the replacement graph.
Algebraic Aspects of Autonomic Systems
Published in Phan Cong Vinh, Nature-Inspired Networking: Theory and Applications, 2018
Given the setup of diagram 1.26, we define the pushout of AS1 and AS2 over AS to be any autonomic system AS3 for which we have an isomorphism AS3→≅AS1⊔ASAS2. The corner symbol “⌜” in diagram 1.26 indicates that AS3 is the pushout.
A set-theoretic proof of the representation of MV-algebras by sheaves
Published in Journal of Applied Non-Classical Logics, 2022
Alejandro Estrada, Yuri A. Poveda
The aim of this paper is to show the duality between MV-algebras and MV-spaces (objects of a geometrical nature, see Definition 5.1), intended for readers who may not be familiar with category theory. Basic knowledge of MV-algebras (we recommend the first chapter of the book (Cignoli et al., 2000)) as well as general topology is necessary to follow the exposition here. We proceed as follows: in Section 2 we highlight the fundamental facts that will be used in the rest of the paper. Section 3 is devoted to the construction of the topological space formed by the prime ideals of an MV-algebra A with the co-Zariski topology. In Section 4, we prove the compactness of using properties of the collections of filters in the MV-algebra. We view these two spaces as point-free topological spaces and establish an isomorphism, thus avoiding the topos theory worked out in Dubuc and Poveda (2010) to prove this compactness. Finally, in Section 5 we establish the representation theorem with an elementary demonstration. We emphasise that instead of using the fact that a certain pushout diagram is also a pullback diagram, as in the Dubuc-Poveda paper (Dubuc & Poveda, 2010, Section 7), we apply the Chinese remainder theorem, which is not surprising due to the connection between the representations by sheaves and the pairwise commuting congruences in distributive lattices (Gehrke, 2018; Vaggione, 1992; Wolf, 1974).
A review on strengthening, delamination formation and suppression techniques during drilling of CFRP composites
Published in Cogent Engineering, 2021
Dhruv Rathod, Mihir Rathod, Ronak Patel, S.M. Shahabaz, S. Divakara Shetty, Nagaraja Shetty
More often in industries drilling using support plates is performed to reduce the delamination despite the higher cycle time and more significant production cost associated with it (Capello, 2004). It was reported that the delamination of the last bottom-most layer along with the neighboring layer of the composite is lowered by 13% and 7%, respectively, when the area of the last ply is reduced from 14 to 6.5 mm. To minimize pushout delamination further, an adjustable active-backup force was set up with the help of an electromagnetic solenoid device to counter the pushout due to thrust force applied by the drill instead of a simple support plate (Tsao et al., 2012). When more complex structures other than a plate are to be manufactured, an electromagnet and a deformable chip colloidal solution of magnetic iron powder is used in tube type parts in industries, which reduces the delamination by about 60–80% (Hocheng et al., 2014).
On the mathematics of higher structures
Published in International Journal of General Systems, 2019
Even if the Ω's and B's (to be defined later in this section) are just general assignments we may ask how they behave with respect to unions and intersections – even if they are not functors. We may look for analogues of pullback and pushout preservation. In many cases, we do not find this, and it may lead to new kinds of mathematical structures. This applies to both Ω and B assignments.