TY - JOUR A1 - Sultanow, Eldar A1 - Weber, Edzard T1 - Prozessleitstände für verteilte und nichtplanbare Organisationsprozesse BT - ein Modell für globales Kollaborations- und Wissensmanagement JF - Handbuch prozessorientiertes Wissensmanagement Y1 - 2014 SN - 978-3-95545-026-7 SP - 335 EP - 344 PB - GITO CY - Berlin ER - TY - JOUR A1 - Sultanow, Eldar A1 - Vladova, Gergana A1 - Weber, Edzard T1 - Overcoming communication barriers for CMC in enterprises Y1 - 2009 SN - 978-0-615-30358-1 ER - TY - JOUR A1 - Sultanow, Eldar A1 - Weber, Edzard T1 - Klassifikation und Identifikation von Kommunikationsbarrieren in Unternehmen Y1 - 2009 SN - 978-3-88579-239-0 ER - TY - JOUR A1 - Sultanow, Eldar A1 - Weber, Edzard T1 - Systeme für Dokumenten-Management (DMS) und Content Management (CMS) : Definitionen und Kategorien Y1 - 2009 SN - 1617-948X ER - TY - JOUR A1 - Sultanow, Eldar A1 - Weber, Edzard T1 - Management-Leitstände 2.0 : Kollaboration, Semantic Web und Web 3D Y1 - 2009 SN - 0945-0491 ER - TY - JOUR A1 - Sultanow, Eldar A1 - Weber, Edzard T1 - Pharmataxigraphie Model of a Hybrid System of RFID Technology and optical Methods JF - Die pharmazeutische Industrie Y1 - 2013 SN - 0031-711X VL - 75 IS - 7 SP - 1197 EP - + PB - Editio-Cantor-Verl. für Medizin und Naturwiss. CY - Aulendorf ER - TY - RPRT A1 - Sultanow, Eldar A1 - Koch, Christian A1 - Cox, Sean T1 - Collatz Sequences in the Light of Graph Theory N2 - 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. KW - Collatz KW - Cayley Graph KW - Free Group KW - Reachability Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-437416 ET - 2nd version ER - TY - RPRT A1 - Sultanow, Eldar A1 - Koch, Christian A1 - Cox, Sean T1 - Collatz Sequences in the Light of Graph Theory N2 - 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. KW - Collatz KW - Cayley Graph KW - Free Group KW - Reachability Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-430089 ER - TY - RPRT A1 - Sultanow, Eldar A1 - Koch, Christian A1 - Cox, Sean T1 - Collatz Sequences in the Light of Graph Theory N2 - 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. KW - Collatz KW - Cayley Graph KW - Free Group KW - Reachability Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-441859 ET - 3rd version ER - TY - RPRT A1 - Sultanow, Eldar A1 - Koch, Christian A1 - Cox, Sean T1 - Collatz Sequences in the Light of Graph Theory N2 - 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. KW - Collatz KW - Cayley Graph KW - Free Group KW - Reachability Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-443254 ET - 4th version ER -