592 research outputs found
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
Wie viel Grenzwert braucht der Mensch? – Unendlichkeit dynamisch und statisch begreifen
Im Alltag bezeichnet ein Grenzwert eine real messbare Größe, die aus
rechtlichen Gründen nicht überschritten werden sollte (z. B. !- oder
Feinstaub-Grenzwert). Demgegenüber zeichnet sich der mathematische
Grenzwertbegriff gerade dadurch aus, ein theoretisches Gedankenkonstrukt
zu sein, welches einem unendlichen Prozess ein idealisiertes Ergebnis zuordnet.
Aus didaktischer Perspektive kann somit die Frage aufgeworfen
werden, inwiefern eine rein theoretische Auseinandersetzung mit Grenzwerten
im Mathematikunterricht überhaupt legitimiert werden kann
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
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 and code length
for given minimum distance 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 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
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
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