A Line-Formula Notation System for Markush Structures

1968 ◽  
Vol 8 (3) ◽  
pp. 173-178
Author(s):  
Helen M. S. Sneed ◽  
James H. Turnipseed ◽  
Robert A. Turpin
Keyword(s):  
Notation System ◽  
Markush Structures

scholarly journals A FIELD GUIDE TO SONIC BOTANY: THOUGHTS ABOUT ECO-COMPOSITION

Tempo ◽  
2020 ◽  
Vol 75 (295) ◽  
pp. 31-44
Author(s):  
Maayan Tsadka
Keyword(s):  
Organic Matter ◽  
Performance Practice ◽  
Musical Instruments ◽  
Musical Composition ◽  
Notation System ◽  
Field Guide ◽  
The Past ◽  
Tuning Forks ◽  
Texture Size ◽  
Ongoing Project

AbstractSonic botany is an ongoing project that I have been developing over the past few years. It incorporates natural artefacts: dry leaves, pods, flowers, branches, rocks, bones and other organic findings. These are used as musical instruments that are played on with a scientific/musical tool: tuning forks in various frequencies. The vibration from the tuning forks resonates through the natural artefacts which amplify the vibration and – via sound – reveal the texture, size, material and condition of the organic matter. This process generates new sonic material, new context and new forms of musical composition. The practice developed into several compositions and projects, a performance practice, a notation system and a way of listening. Here I share some of the insights I gained through this process, the tools and the compositional framework.

A Buchholz derivation system for the ordinal analysis of KP + Π3-reflection

2006 ◽  
Vol 71 (4) ◽  
pp. 1237-1283
Author(s):  
Markus Michelbrink
Keyword(s):  
Ordinal Analysis ◽  
Notation System ◽  
Recursive Functions ◽  
Conservation Result ◽  
Ordinal Notation

AbstractIn this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP + Π3-Reflection due to Michael Rathjen. This allows a finitary ordinal analysis of KP + Π3-Reflection. The method used is an extension of techniques developed by Wilfried Buchholz, namely operator controlled notation systems for RS∞-derivations. Similarly to Buchholz we obtain a characterisation of the provably recursive functions of KP + Π3-Reflection as <-recursive functions where < is the ordering on Rathjen's ordinal notation system . Further we show a conservation result for -sentences.

scholarly journals Remarks on the usefulness of different types of transcription, with a particular regard to Turkic comparative studies

2011 ◽  
Vol 2011 (93) ◽  
Author(s):  
Kamil Stachowski
Keyword(s):  
Comparative Studies ◽  
Notation System ◽  
Level Of Abstraction ◽  
Different Types

The article attempts to determine what kind of transcription is best suited for (Turkic) comparative studies. Five questions are asked: what are the features of an ideal transcription, what level of abstraction is most useful, what notation system is most practical, and is it possible for a single transcription to encompass the entire Turkic family. Ultimately, a set of basic rules is proposed together with a small exemplification. 

Ordinal notations and induction

2021 ◽  
pp. 312-345
Author(s):  
Paolo Mancosu ◽  
Sergio Galvan ◽  
Richard Zach
Keyword(s):  
Simple Proof ◽  
Cut Elimination ◽  
Notation System ◽  
Ordinal Notations ◽  
Combinatorial System

In order to prove that the simplification process for arithmetic eventually reaches a simple proof, it is necessary to measure the complexity of proofs in a more sophisticated way than for the cut-elimination theorem. There, a pair of numbers suffices, and the proof proceeds by double induction on this measure. This chapter develops the system of ordinal notations up to ε0 which serve as this more sophisticated measure for proofs in arithmetic. Ordinal notations are presented as purely combinatorial system of symbols, so that from the outset there is no doubt about the constructive legitimacy of the associated principles of reasoning. The main properties of this notation system are presented, and it is shown that ordinal notations are well-ordered according to its associated less-than relation. The basics of the theory of set-theoretic ordinals is developed in the second half of the chapter, so that the reader can compare the infinitary, set-theoretic development of ordinals up to ε0 to the system of finitary ordinal notations. Finally, Paris-Kirby Hydra game and Goodstein sequences are presented as applications of induction up to ε0.

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