Search results for "Axiomatic"
showing 10 items of 13 documents
Complex powers and non-compact manifolds
2002
We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras, ``extended Weyl algebras,'' whose definition was inspired by Guillemin's paper on the subject. An extended Weyl algebra can be thought of as an algebra of ``abstract pseudodifferential operators.'' Many algebras of pseudodifferential operators are extended Weyl algebras. Several results typical for algebras of pseudodifferential operators (asymptotic completeness, construction of Sobolev spaces, boundedness between apropriate Sobolev spaces, >...) generalize to…
Urban poverty: Measurement theory and evidence from American cities
2021
AbstractWe characterize axiomatically a new index of urban poverty that i) captures aspects of the incidence and distribution of poverty across neighborhoods of a city, ii) is related to the Gini index and iii) is consistent with empirical evidence that living in a high poverty neighborhood is detrimental for many dimensions of residents’ well-being. Widely adopted measures of urban poverty, such as the concentrated poverty index, may violate some of the desirable properties we outline. Furthermore, we show that changes of urban poverty within the same city are additively decomposable into the contribution of demographic, convergence, re-ranking and spatial effects. We collect new evidence …
Axiomatic Foundations Of Fixed-Basis Fuzzy Topology
1999
This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory. In general we do not pursue the historical development, but it is our primary aim to present the state of the art of this field. We focus on the following problems:
The Calm Before the Storm: Hilbert’s Early Views on Foundations
2000
In recent years there has been a growing interest among historians and philosophers of mathematics in the history of logic, set theory, and foundations.1 This trend has led to a major reassessment of early work undertaken in these fields, particularly when seen in the light of motivations that animated the leading actors. The present volume may thus be seen as a reflection of this renewed fascination with the work of Hilbert, Brouwer, Weyl, Bernays, and others, an interest that stems in part from the desire to understand the historical and intellectual context that inspired their investigations. With regard to Hilbert, it has been my contention for some time that his stance in the acrimonio…
The Obstacle Problem in a Non-Linear Potential Theory
1988
M. Brelot gave rise to the concept harmonic space when he extended classical potential theory on ℝn to an axiomatic system on a locally compact space. I have recently constructed1 a non-linear harmonic space by dropping the assumption that the sum of two harmonic functions is harmonic and considering some other axioms instead. This approach has its origin in the work of O. Martio, P. Lindqvist and S. Granlund2,3,4, who have developed a non-linear potential theory on ℝn connected with variational integrals of the type ∫ F(x,∇u(x)) dm(x), where F(x, h) ≈ |h|p.
A Measure of Polarization for Tourism: Evidence from Italian Destinations
2011
This paper proposes an index of polarization for tourism which links the axiomatic theory of Esteban and Ray with the classical hierarchical agglomerative clustering techniques. The index is aimed at analyzing the dynamics of the average length of stay across Italian destinations, and more specifically to detect whether the polarization within the set of clusters of places with similar values of the indicator has varied over time.
A Design Theory for Secure Information Systems Design Methods
2006
Many alternative methods for designing secure information systems (SIS) have been proposed to ensure system security. However, within all the literature on SIS methods, there exists little theoretically grounded work that addresses the fundamental requirements and goals of SIS design. This paper first uses design theory to develop a SIS design theory framework that defines six requirements for SIS design methods, and second, shows how known SIS design methods fail to satisfy these requirements. Third, the paper describes a SIS design method that does address these requirements and reports two empirical studies that demonstrate the validity of the proposed framework. peerReviewed
Basic Mathematical Thinking
2016
Mathematics, from the Greek word “mathema”, is simply translated as science or expression of the knowledge.
Comparative Reasoning for Intelligent Agents
2023
We demonstrate new comparative reasoning abilities of NARS, a formal model of intelligence, which enable the asymmetric comparison of perceivable quantifiable attributes of objects using rela- tions. These new abilities are implemented by extending NAL with addi- tional inference rules. We demonstrate the new capabilities in a bottle- picking experiment on a mobile robot running ONA, an implementation of NARS.
Differential structure associated to axiomatic Sobolev spaces
2020
The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure. peerReviewed