Search results for "Set theory"
showing 10 items of 751 documents
Statistical analysis of life history calendar data
2016
The life history calendar is a data-collection tool for obtaining reliable retrospective data about life events. To illustrate the analysis of such data, we compare the model-based probabilistic event history analysis and the model-free data mining method, sequence analysis. In event history analysis, we estimate instead of transition hazards the cumulative prediction probabilities of life events in the entire trajectory. In sequence analysis, we compare several dissimilarity metrics and contrast data-driven and user-defined substitution costs. As an example, we study young adults' transition to adulthood as a sequence of events in three life domains. The events define the multistate event…
Split-Window Coefficients for Land Surface Temperature Retrieval From Low-Resolution Thermal Infrared Sensors
2008
In this letter, we provide a complete set of split-window coefficients that can be used to retrieve land surface temperature (LST) from thermal infrared sensors onboard the most popular remote-sensing satellites: ERS-ATSR2, ENVISAT-AATSR, Terra/Aqua-MODIS, NOAA series-AVHRR, METOP-AVHRR3, GOES series-IMAGER, and MSG1/MSG2-SEVIRI. The coefficients have been obtained by minimization from an extensive simulated database constructed from MODTRAN radiative transfer code calculations, emissivity spectra extracted from spectral libraries, and spectral response functions of the thermal bands considered. This letter also analyzes the magnitude of the error on the LST retrieval and the contribution t…
Cardinal estimates involving the weak Lindelöf game
2021
AbstractWe show that if X is a first-countable Urysohn space where player II has a winning strategy in the game $$G^{\omega _1}_1({\mathcal {O}}, {\mathcal {O}}_D)$$ G 1 ω 1 ( O , O D ) (the weak Lindelöf game of length $$\omega _1$$ ω 1 ) then X has cardinality at most continuum. This may be considered a partial answer to an old question of Bell, Ginsburg and Woods. It is also the best result of this kind since there are Hausdorff first-countable spaces of arbitrarily large cardinality where player II has a winning strategy even in the weak Lindelöf game of countable length. We also tackle the problem of finding a bound on the cardinality of a first-countable space where player II has a wi…
The Classical Theory of Real Functions
1998
The first class of real functions we deal with in this chapter is the class of functions of locally finite variation. These functions are closely related to the real measures on B. Exploiting this connection would allow us to obtain the properties of these functions from the general results in Chapter 4. But the path we follow here is a more direct one which applies the theory of vector lattices. The link with the measures on B will be established in the next section.
Polaroid operators and Weyl type theorems
2015
Weyl type theorems have been proved for a considerably large number of classes of operators. In this work, after introducing the class of polaroid operators and some notions from local spectral theory, we determine a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. The theory is exemplified by given several examples of hereditarily polaroid operators.
Nonstochastic languages as projections of 2-tape quasideterministic languages
1998
A language L (n) of n-tuples of words which is recognized by a n-tape rational finite-probabilistic automaton with probability 1-e, for arbitrary e > 0, is called quasideterministic. It is proved in [Fr 81], that each rational stochastic language is a projection of a quasideterministic language L (n) of n-tuples of words. Had projections of quasideterministic languages on one tape always been rational stochastic languages, we would have a good characterization of the class of the rational stochastic languages. However we prove the opposite in this paper. A two-tape quasideterministic language exists, the projection of which on the first tape is a nonstochastic language.
Algebraic and logical characterizations of deterministic linear time classes
1997
In this paper an algebraic characterization of the class DLIN of functions that can be computed in linear time by a deterministic RAM using only numbers of linear size is given. This class was introduced by Grandjean, who showed that it is robust and contains most computational problems that are usually considered to be solvable in deterministic linear time.
FORMAL CONCEPTION OF ROUGH SETS
1996
In the paper we present a formal description of rough sets within the framework of the generalized set theory, which is interpreted in the set approximation theory. The rough sets are interpreted as approximations, which are defined by means of the Pawlak's rough sets.
Representations of Certain Banach C*-modules
2004
The possibility of extending the well known Gelfand–Naimark– Segal representation of *-algebras to certain Banach C*-modules is studied. For this aim the notion of modular biweight on a Banach C*-module is introduced. For the particular class of strict pre CQ*-algebras, two different types of representations are investigated.
PIP-Spaces and Signal Processing
2009
Contemporary signal processing makes an extensive use of function spaces, always with the aim of getting a precise control on smoothness and decay properties of functions. In this chapter, we will discuss several classes of such function spaces that have found interesting applications, namely, mixed-norm spaces, amalgam spaces, modulation spaces, or Besov spaces. It turns out that all those spaces come in families indexed by one or more parameters, that specify, for instance, the local behavior or the asymptotic properties. In general, a single space, taken alone, does not have an intrinsic meaning, it is the family as a whole that does, which brings us to the very topic of this volume. In …