scholarly journals A Uniform Approach to Complexes arising from Forests

10.37236/825 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Mario Marietti ◽  
Damiano Testa
Keyword(s):  
Homotopy Type ◽  
Uniform Approach

In this paper we present a unifying approach to study the homotopy type of several complexes arising from forests. We show that this method applies uniformly to many complexes that have been extensively studied in the recent years.

The smooth case

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Homotopy Type ◽  
Unit Vector ◽  
Smooth Case ◽  
Open Set ◽  
Birational Invariant

This chapter examines the simplifications occurring in the proof of the main theorem in the smooth case. It begins by stating the theorem about the existence of an F-definable homotopy h : I × unit vector X → unit vector X and the properties for h. It then presents the proof, which depends on two lemmas. The first recaps the proof of Theorem 11.1.1, but on a Zariski dense open set V₀ only. The second uses smoothness to enable a stronger form of inflation, serving to move into V₀. The chapter also considers the birational character of the definable homotopy type in Remark 12.2.4 concerning a birational invariant.

A uniform approach to static replication

1998 ◽  
Vol 1 (1) ◽  
pp. 73-87 ◽  
Author(s):  
Andrew Chou ◽  
Galin Georgiev
Keyword(s):  
Uniform Approach

scholarly journals Governing information technology (IT) investment: A contingency perspective on organization’s IT investment goals

2021 ◽  
pp. 031289622110095
Author(s):  
Syaiful Ali ◽  
Peter Green ◽  
Alastair Robb ◽  
Adi Masli
Keyword(s):  
Information Technology ◽  
Boards Of Directors ◽  
Contingency Theory ◽  
Jel Classification ◽  
It Investment ◽  
It Investments ◽  
Contingency Perspective ◽  
Uniform Approach ◽  
Business Executives

Using contingency theory, we argue that there is not a uniform approach for companies to govern information technology (IT) investments. Rather, the level of governance over IT investments is contingent upon the organization’s goals for its IT investments. We find that Australian organizations with both operation- and market-focused IT investment goals (i.e. dual-focused IT goals) demonstrate higher IT investment governance (ITIG) levels than those with less focused IT goals. We also document that dual-IT-focused firms that do not implement high levels of ITIG underperform. Our study informs business executives, boards of directors, and other practitioners interested in governance implementations over IT investments. JEL Classification: M1

scholarly journals Hadamard Matrices with Cocyclic Core

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 857
Author(s):  
Víctor Álvarez ◽  
José Andrés Armario ◽  
María Dolores Frau ◽  
Félix Gudiel ◽  
María Belén Güemes ◽  
...  
Keyword(s):  
Hadamard Matrices ◽  
Combinatorial Designs ◽  
Powerful Technique ◽  
Uniform Approach ◽  
Structured Approach

Since Horadam and de Launey introduced the cocyclic framework on combinatorial designs in the 1990s, it has revealed itself as a powerful technique for looking for (cocyclic) Hadamard matrices. Ten years later, the series of papers by Kotsireas, Koukouvinos and Seberry about Hadamard matrices with one or two circulant cores introduced a different structured approach to the Hadamard conjecture. This paper is built on both strengths, so that Hadamard matrices with cocyclic cores are introduced and studied. They are proved to strictly include usual Hadamard matrices with one and two circulant cores, and therefore provide a wiser uniform approach to a structured Hadamard conjecture.

scholarly journals Homotopy type-theoretic interpretations of constructive set theories

2019 ◽  
pp. 1-32
Author(s):  
Cesare Gallozzi
Keyword(s):  
Comparative Analysis ◽  
Set Theory ◽  
Homotopy Type ◽  
Type Theory ◽  
Axiom Of Choice ◽  
Homotopy Type Theory ◽  
Constructive Set Theory

Abstract We introduce a family of (k, h)-interpretations for 2 ≤ k ≤ ∞ and 1 ≤ h ≤ ∞ of constructive set theory into type theory, in which sets and formulas are interpreted as types of homotopy level k and h, respectively. Depending on the values of the parameters k and h, we are able to interpret different theories, like Aczel’s CZF and Myhill’s CST. We also define a proposition-as-hproposition interpretation in the context of logic-enriched type theories. The rest of the paper is devoted to characterising and analysing the interpretations considered. The formulas valid in the prop-as-hprop interpretation are characterised in terms of the axiom of unique choice. We also analyse the interpretations of CST into homotopy type theory, providing a comparative analysis with Aczel’s interpretation. This is done by formulating in a logic-enriched type theory the key principles used in the proofs of the two interpretations. Finally, we characterise a class of sentences valid in the (k, ∞)-interpretations in terms of the ΠΣ axiom of choice.

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