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

This is a reissue of the book Tree Automata by F G\'ecseg and M Steinby originally published in 1984 by Akad\'emiai Kiad\'o, Budapest Some mistakes have been corrected and a few obscure passages have been clarified Moreover, some more recent contributions and current lines of research are reviewed in an appendix that also contains several new references

Tree automata

/pdf/infinite-abelian-groups-2dvcz0046a.pdf

Infinite Abelian Groups

Publisher Summary This chapter presents three mathematical tools that can be used to describe graph-grammars and the sets generated by them. The chapter describes graph properties by logical formulas and presents a comparison of the powers of several logical languages. The chapter discusses first-order logic, second-order logic, and monadic second-order logic, together with a few variants and restrictions of these three languages. It presents algebraic techniques that are useful for defining and studying graph rewriting rules and context-free graph-grammars. The chapter also presents the use of category theory for specifying graph rewriting rules in a precise and concise way, and for properly defining the least or rather the initial solution of a system of graph equations. It presents some links between the context-free graph-grammars and monadic second-order logic. Some applications to the definition of sets of graphs by forbidden configurations and to the theory of NP-completeness are also presented in the chapter.

Graph Rewriting: An Algebraic and Logic Approach.

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand’s ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibilit...

/pdf/the-category-theoretic-solution-of-recursive-domain-5b7t1k4u0s.pdf

The Category-Theoretic Solution of Recursive Domain Equations

Abstract and concrete categories

Free algebras and automata realizations in the language of categories

Iterative theories, which were introduced by Calvin Elgot, formalise potentially infinite computations as unique solutions of recursive equations One of the main results of Elgot and his coauthors is a description of a free iterative theory as the theory of all rational trees Their algebraic proof of this fact is extremely complicated In our paper we show that by starting with ‘iterative algebras’, that is, algebras admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iterative algebras The (coalgebraic) proof we present is dramatically simpler than the original algebraic one Despite this, our result is much more general: we describe a free iterative theory on any finitary endofunctor of every locally presentable category $\cal{A}$Reportedly, a blow from the welterweight boxer Norman Selby, also known as Kid McCoy, left one victim proclaiming,‘It's the real McCoy!’

Iterative algebras at work

On the greatest fixed point of a set functor

http://www.math.uni-bremen.de/~porst/dvis/TreeCoalgsTCS.pdf

Jiří Adámek

Papers

Abstract and concrete categories

Free algebras and automata realizations in the language of categories

Iterative algebras at work

On the greatest fixed point of a set functor

On tree coalgebras and coalgebra presentations