There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

[서평]「Component Software」 - Beyond Object-Oriented Programming -

Handbook of logic in computer science.

The B Book

The concept of algebraic high-level net transformation systems combines two important lines of research recently introduced in the literature: algebraic high-level nets (AHL-nets for short) and high-level replacement systems (HLR-systems for short). In both cases a categorical formulation of the corresponding theory has turned out to be highly important and is also a good basis for the integration of these concepts in this paper.AHL-nets combine Petri nets with algebraic specifications and provide a powerful specification technique for distributed systems including data types and processes.HLR-systems are transformation systems for high-level structures such as graphs, hypergraphs, algebraic specifications and different kinds of Petri nets. The theory of HLRsystems - formulated already in a categorical framework - is applied in this paper to AHLnets. Thus we obtain AHL-net transformation systems as an instantiation of HLR-systems to AHL-nets. This allows us to build up AHL-nets from basic components and to transform the net structure using rules or productions in the sense of graph grammars. This concept is illustrated by extending the well-known example of ‘dining philosophers’. We are able to show that AHL-net-transformation systems satisfy several important compatibility properties. On the one hand we obtain a local Church-Rosser and Parallelism Theorem, which is well-known for graph grammars and has recently been generalized to HLR-systems. This allows us to analyse concurrency in AHL-nets not only on the token level but also on the level of transformations of the net structure. On the other hand, we consider the ‘fusion’ and ‘union’ constructions for high-level structures, motivated by corresponding concepts for high-level Petri nets in the literature, and we show compatibility of these constructions with derivations of HLR-systems in general and AHL-nettransformations in particular. This means compatibility of vertical and horizontal structuring in terms of software development.

Algebraic high-level net transformation systems

Adhesive high-level replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobocinski.

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Adhesive High-Level Replacement Categories and Systems

Adhesive high-level replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobocinacute;ski. 

In this paper we show that most of the HLR properties, which had been introduced to generalize some basic results from the category of graphs to high-level structures, are valid already in adhesive HLR categories. This leads to a smooth categorical theory of HLR systems which can be applied to a large variety of graphs and other visual models. As a main new result in a categorical framework we show the Critical Pair Lemma for the local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.

Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation

The increasing number of Petri net variants naturally leads to the question whether the term “Petri net” is more than a common name for very different concepts. This contribution tries to identify aspects common to all or at least to most Petri nets. It concentrates on those features where Petri nets significantly differ from other modeling languages, i.e. we ask where the use of Petri nets leads to advantages compared to other languages. Different techniques that are usually comprised under the header “analysis” are distinguished with respect to the analysis aim. Finally, the role of Petri nets in the development of distributed systems is discussed.

Unifying Petri Nets

The aim of this paper is a tutorial introduction to graph grammars and graph transformations on one hand and to Petri net transformations on the other hand. In addition to an introduction to both areas the paper shows how they have influenced each other. The concurrency concepts and semantics of graph transformations have been generalized from those of Petri net using the fact that the token game of Petri nets can be considered as a graph transformation step on discrete graphs. On the other hand each Petri net can be considered as a graph, such that graph transformations can be used to change the net structure of Petri nets. This leads to a rule based approach for the development of Petri nets, where the nets in different development stages are related by Petri net transformations.

Julia Padberg

Papers

Algebraic high-level net transformation systems

Adhesive High-Level Replacement Categories and Systems

Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation

Unifying Petri Nets

Graph Grammars and Petri Net Transformations