A result on polynomials derived via graph theory

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that some trinomials over finite fields have the same number of roots

Entwicklungsstufen des Unternehmensarchitekturmanagements

Zusammenfassungen: Je nach Ausgestaltung kann Unternehmensarchitekturmanagement (UAM) eine wichtige Komponente des strategischen IT-Managements bilden — oder auch nicht. Um die Ausgestaltungsmöglichkeiten besser zu verstehen, führen wir zunächst UAM-Dimensionen ein und beschreiben auf dieser Grundlage vier zentrale UAM-Entwick-lungsstufen, deren letzte >>strategisches UAM<< ist. Die vier Entwicklungsstufen ermöglichen dem Leser die Positionierung des jeweils realisierten UAM im eigenen Unternehmen sowie die Definition eines angemessenen Zielzustands. Drei Kurzfallstudien zeigen konkret auf, in welchen Variationen strategisches UAM umgesetzt und in welcher Weise dadurch strategisches Informationsmanagement unterstützt werden kan

Method Support of Information Requirements Analysis for Analytical Information Systems: State of the Art, Practice Requirements, and Research Agenda

Due to specific characteristics of analytical information systems, their development varies significantly from transaction-oriented systems. Specific method support is particularly needed for requirements engineering and its information-related component, information requirements analysis. The paper at hand first evaluates the state of the art and identifies necessary method support extensions. On this basis, method support requirements for information requirements engineering are identified. The survey is structured along the five core activities of traditional requirements engineering. It reveals a need for further research especially on information requirements elicitation, validation, and management. It further contributes to a discussion of aspects that should be considered by any method support. Due to comparatively long life cycles of analytical information systems, the introduction of a process perspective is discussed in order to ensure the continuous elicitation, documentation, and management of information requirement

Whom to Inform about Prices? Evidence from the German Fuel Market

Combining a theoretical model of imperfect information with empirical evidence, we show how the effect of providing price information to consumers depends on how well informed they are beforehand. Theoretically, an increase in consumer information decreases prices more, the fewer ex ante informed consumers there are. Empirically, we study mandatory price disclosure in the German fuel market for two fuel types that differ in ex ante consumer information. The decline in prices is stronger when there are fewer ex ante informed consumers. The magnitude of the treatment effect declines over time but is intensified by local follow-on information campaigns

Method Support of Information Requirements Analysis for Analytical Information Systems State of the Art, Practice Requirements, and Research Agenda

Due to specific characteristics of analyticalinformation systems, their developmentvaries significantly from transaction-oriented systems. Specific methodsupport is particularly needed forrequirements engineering and itsinformation-related component, informationrequirements analysis. The paperat hand first evaluates the state ofthe art and identifies necessary methodsupport extensions.On this basis,methodsupport requirements for informationrequirements engineering are identified.The survey is structured alongthe five core activities of traditional requirementsengineering. It reveals aneed for further research especially oninformation requirements elicitation,validation, and management. It furthercontributes to a discussion of aspectsthat should be considered by anymethod support. Due to comparativelylong life cycles of analytical informationsystems, the introduction of a processperspective is discussed in order to ensurethe continuous elicitation, documentation,and management of informationrequirements

Entropic proofs of Singleton bounds for quantum error-correcting codes

We show that a relatively simple reasoning using von Neumann entropy inequalities yields a robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC). For entanglement-assisted quantum error-correcting codes (EAQECC) and catalytic codes (CQECC), a type of generalized quantum Singleton bound [Brun et al., IEEE Trans. Inf. Theory 60(6):3073--3089 (2014)] was believed to hold for many years until recently one of us found a counterexample [MG, Phys. Rev. A 103, 020601 (2021)]. Here, we rectify this state of affairs by proving the correct generalized quantum Singleton bound, extending the above-mentioned proof method for QECC; we also prove information-theoretically tight bounds on the entanglement-communication tradeoff for EAQECC. All of the bounds relate block length $n$ and code length $k$ for given minimum distance $d$ and we show that they are robust, in the sense that they hold with small perturbations for codes which only correct most of the erasure errors of less than $d$ letters. In contrast to the classical case, the bounds take on qualitatively different forms depending on whether the minimum distance is smaller or larger than half the block length. We also provide a propagation rule: any pure QECC yields an EAQECC with the same distance and dimension, but of shorter block length.Comment: 14 pages, 5 figures. Theorem 7 and Corollaries 8 and 9 adde

An extremal characterization of projective planes

In this article, we prove that amongst all n by n bipartite graphs of girth at least six, where n = q(2) + q + 1 >= 157, the incidence graph of a projective plane of order q, when it exists, has the maximum number of cycles of length eight. This characterizes projective planes as the partial planes with the maximum number of quadrilaterals