@phdthesis{Sultanow2015,
author = {Sultanow, Eldar},
title = {Real World Awareness in kollaborativen Unternehmensprozessen},
series = {Schriften der Forschungsvereinigung Software ; 3},
journal = {Schriften der Forschungsvereinigung Software ; 3},
publisher = {GITO},
address = {Berlin},
isbn = {978-3-95545-118-9},
pages = {221},
year = {2015},
language = {de}
}
@article{SultanowVladovaWeber2009,
author = {Sultanow, Eldar and Vladova, Gergana and Weber, Edzard},
title = {Overcoming communication barriers for CMC in enterprises},
isbn = {978-0-615-30358-1},
year = {2009},
language = {en}
}
@article{FroemingGronauSultanow2008,
author = {Fr{\"o}ming, Jane and Gronau, Norbert and Sultanow, Eldar},
title = {MDA-Werkzeuge : Softwareautomaten ; im Vergleich: jABC, AndroMDA und OpenArchitectureWare},
issn = {0935-9680},
year = {2008},
language = {de}
}
@article{BrockmannGronauSultanow2008,
author = {Brockmann, Carsten and Gronau, Norbert and Sultanow, Eldar},
title = {ERP und MES : Teil 3},
issn = {1617-948X},
year = {2008},
language = {de}
}
@article{SultanowWeber2009,
author = {Sultanow, Eldar and Weber, Edzard},
title = {Klassifikation und Identifikation von Kommunikationsbarrieren in Unternehmen},
isbn = {978-3-88579-239-0},
year = {2009},
language = {de}
}
@article{SultanowWeber2009,
author = {Sultanow, Eldar and Weber, Edzard},
title = {Systeme f{\"u}r Dokumenten-Management (DMS) und Content Management (CMS) : Definitionen und Kategorien},
issn = {1617-948X},
year = {2009},
language = {de}
}
@article{SultanowWeber2009,
author = {Sultanow, Eldar and Weber, Edzard},
title = {Management-Leitst{\"a}nde 2.0 : Kollaboration, Semantic Web und Web 3D},
issn = {0945-0491},
year = {2009},
language = {de}
}
@article{SultanowWeber2013,
author = {Sultanow, Eldar and Weber, Edzard},
title = {Pharmataxigraphie Model of a Hybrid System of RFID Technology and optical Methods},
series = {Die pharmazeutische Industrie},
volume = {75},
journal = {Die pharmazeutische Industrie},
number = {7},
publisher = {Editio-Cantor-Verl. f{\"u}r Medizin und Naturwiss.},
address = {Aulendorf},
issn = {0031-711X},
pages = {1197 -- +},
year = {2013},
language = {de}
}
@techreport{SultanowVolkovCox2017,
author = {Sultanow, Eldar and Volkov, Denis and Cox, Sean},
title = {Introducing a Finite State Machine for processing Collatz Sequences},
edition = {1st version},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-399223},
year = {2017},
abstract = {The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine's word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.},
language = {en}
}
@techreport{SultanowVolkovCox2017,
author = {Sultanow, Eldar and Volkov, Denis and Cox, Sean},
title = {Introducing a Finite State Machine for processing Collatz Sequences},
edition = {2nd version},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-404738},
pages = {17},
year = {2017},
abstract = {The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine's word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.},
language = {en}
}
@article{SultanowWeber2014,
author = {Sultanow, Eldar and Weber, Edzard},
title = {Prozessleitst{\"a}nde f{\"u}r verteilte und nichtplanbare Organisationsprozesse},
series = {Handbuch prozessorientiertes Wissensmanagement},
journal = {Handbuch prozessorientiertes Wissensmanagement},
publisher = {GITO},
address = {Berlin},
isbn = {978-3-95545-026-7},
pages = {335 -- 344},
year = {2014},
language = {de}
}
@techreport{SultanowKochCox2019,
author = {Sultanow, Eldar and Koch, Christian and Cox, Sean},
title = {Collatz Sequences in the Light of Graph Theory},
doi = {10.25932/publishup-43008},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-430089},
pages = {15},
year = {2019},
abstract = {The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.},
language = {en}
}
@techreport{SultanowKochCox2020,
author = {Sultanow, Eldar and Koch, Christian and Cox, Sean},
title = {Collatz Sequences in the Light of Graph Theory},
edition = {3rd version},
doi = {10.25932/publishup-44185},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441859},
pages = {29},
year = {2020},
abstract = {It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all (odd) natural numbers. A structured reachability analysis is hitherto not available. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. The analysis of this tree will provide new insights into the structure of Collatz sequences. The findings are of special interest to possible cycles within a sequence. Next, we describe the conditions which must be fulfilled by a cycle. Finally, we demonstrate how these conditions could be used to prove that the only possible cycle within a Collatz sequence is the trivial cycle, starting with the number 1, as conjectured by Lothar Collatz.},
language = {en}
}
@techreport{SultanowKochCox2019,
author = {Sultanow, Eldar and Koch, Christian and Cox, Sean},
title = {Collatz Sequences in the Light of Graph Theory},
edition = {2nd version},
doi = {10.25932/publishup-43741},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437416},
pages = {21},
year = {2019},
abstract = {The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequence's "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.},
language = {en}
}
@techreport{SultanowKochCox2020,
author = {Sultanow, Eldar and Koch, Christian and Cox, Sean},
title = {Collatz Sequences in the Light of Graph Theory},
edition = {4th version},
doi = {10.25932/publishup-44325},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-443254},
pages = {31},
year = {2020},
abstract = {It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all odd natural numbers. A structured reachability analysis is hitherto not available. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. The analysis of this tree will provide new insights into the structure of Collatz sequences. The findings are of special interest to possible cycles within a sequence. Next, we describe the conditions which must be fulfilled by a cycle. Finally, we demonstrate how these conditions could be used to prove that the only possible cycle within a Collatz sequence is the trivial cycle, starting with the number one, as conjectured by Lothar Collatz.},
language = {en}
}
@techreport{SultanowKochCox2020,
author = {Sultanow, Eldar and Koch, Christian and Cox, Sean},
title = {Collatz Sequences in the Light of Graph Theory},
edition = {Fifth version},
doi = {10.25932/publishup-48214},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-482140},
pages = {47},
year = {2020},
abstract = {It is well known that the inverted Collatz sequence can be represented as a graph or a tree. Similarly, it is acknowledged that in order to prove the Collatz conjecture, one must demonstrate that this tree covers all odd natural numbers. A structured reachability analysis is hitherto unavailable. This paper investigates the problem from a graph theory perspective. We define a tree that consists of nodes labeled with Collatz sequence numbers. This tree will be transformed into a sub-tree that only contains odd labeled nodes. Furthermore, we derive and prove several formulas that can be used to traverse the graph. The analysis covers the Collatz problem both in it's original form 3x + 1 as well as in the generalized variant kx + 1. Finally, we transform the Collatz graph into a binary tree, following the approach of Kleinnijenhuis, which could form the basis for a comprehensive proof of the conjecture.},
language = {en}
}