Results 1 to 10 of about 30,932 (176)
Nonstandard Methods in Measure Theory [PDF]
Abstract and Applied Analysis, 2014 Ideas and techniques from standard and nonstandard theories of measure spaces and Banach spaces are brought together to give a new approach to the study of the extension of vector measures.
Grigore Ciurea
doaj +4 more sources
Self-calibration technique for characterization of integrated THz waveguides
Physical Review Accelerators and Beams, 2021 Emerging high-frequency accelerator technology in the terahertz regime is promising for the development of compact high-brightness accelerators and high resolution–power beam diagnostics. One resounding challenge when scaling to higher frequencies and to
M. Kellermeier +4 more
doaj +1 more source
CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES
The Bulletin of Symbolic Logic, 2022 AbstractCurrently the two popular ways to practice Robinson’s nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions relying on external sets.
KAREL HRBACEK, MIKHAIL G. KATZ
openaire +2 more sources
Nonstandard Measure Theory-Hausdorff Measure [PDF]
Proceedings of the American Mathematical Society, 1977 In this paper it is shown that the Hausdorff measures λ t {\lambda ^t} for t ∈ [ 0 , ∞ ) t \in [0,\infty ) can be simultaneously represented as ∗ ^\ast finite counting measures in an appropriate ...
openaire +2 more sources
A Nonstandard Neutrosophic Model for Aesthetic Response in Interactive Device Decorative Art Design [PDF]
Neutrosophic Sets and SystemsThis paper introduces a new mathematical model called the Nonstandard Neutrosophic Aesthetic Dynamics (NSNAD). It is built using nonstandard neutrosophic theory, which allows us to work with values that are greater than 1, less than 0, or undefined ...
Xing Wei
doaj +1 more source
Phase Operator Problem and Macroscopic Extension of Quantum Mechanics [PDF]
, 1997 To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis.
Abe +38 more
core +1 more source
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [PDF]
, 2017 The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.Comment: 126 pages.
Di Nasso, Mauro +2 more
core +2 more sources
IEEE Access, 2019 This paper aims at developing a novel generalized distance measure of Pythagorean fuzzy (PF) sets and constructing a distance-based compromise approach for multiple criteria decision analysis (MCDA) within PF environments.
Ting-Yu Chen
doaj +1 more source
Nonstandard Measure Theory: Avoiding Pathological Sets [PDF]
Transactions of the American Mathematical Society, 1979 The main results in this paper concern representing Lebesgue measure by nonstandard measures which avoid certain pathological sets. An (external) set E is S-thin if InfmA|A standard,* A ⊇ E A\, \supseteq \,E = 0 and Q-thin if Inf*mA|A internal, A ⊇ E
openaire +1 more source
Lifting Theorems in Nonstandard Measure Theory [PDF]
Proceedings of the American Mathematical Society, 1990 1. A nonstandard capacity construction, analogous to Loeb’s measure construction, is developed. Using this construction and Choquet’s Capacitability theorem, it is proved that a Loeb measurable function into a general (not necessarily second countable) space has a lifting precisely when its graph is ’almost’ analytic.
openaire +1 more source