Search results for "continuum"
showing 10 items of 477 documents
Rolewicz-type chaotic operators
2015
In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.
PRINZIPIELLE BEMERKUNGEN ZU THEORIE UND PRAXIS DER METHODE DER ZWEITEN ABLEITUNG BEI DER INTERPRETATION GRAVIMETRISCHER MESSERGEBNISSE
1957
The first part of the paper deals with theoretical considerations concerning the arithmetic mean of gravity values and its use with regard to the derivation of approximation formulae for the second derivative. In order to calculate the second derivative in practice the arithmetic mean. ḡ(r) of a continuum of gravity values on a circle of radius r is approximated by a Taylor polynomial and then replaced by the arithmetic mean gn(r) of n discrete gravity values. Because of the invariance of ġ(r) with regard to rotations of the coordinate system in the horizontal datum plane there exists a lower limit for the number n; this lower limit depends on the degree of the Taylor polynomial used in the…
A Tomographical Characterization of L-convex Polyominoes
2005
Our main purpose is to characterize the class of L-convex polyominoes introduced in [3] by means of their horizontal and vertical projections. The achieved results allow an answer to one of the most relevant questions in tomography i.e. the uniqueness of discrete sets, with respect to their horizontal and vertical projections. In this paper, by giving a characterization of L-convex polyominoes, we investigate the connection between uniqueness property and unimodality of vectors of horizontal and vertical projections. In the last section we consider the continuum environment; we extend the definition of L-convex set, and we obtain some results analogous to those for the discrete case.
Selective versions of chain condition-type properties
2015
We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal invariants of the continuum.
Monotonicity and total boundednessin spaces of measurable functions
2017
Abstract We define and study the moduli d(x, 𝓐, D) and i(x, 𝓐,D) related to monotonicity of a given function x of the space L 0(Ω) of real-valued “measurable” functions defined on a linearly ordered set Ω. We extend the definitions to subsets X of L 0(Ω), and we use the obtained quantities, d(X) and i(X), to estimate the Hausdorff measure of noncompactness γ(X) of X. Compactness criteria, in special cases, are obtained.
Feynman-Kac formulae
2015
In this chapter, we establish the connection between the deterministic EIT forward problem and the class of reflecting diffusion processes. We proceed along the lines of the recent paper [137] by Piiroinen and the author: We derive Feynman-Kac formulae in terms of these processes for the solutions to the forward problems corresponding to the continuum model and the complete electrode model, respectively. These results extend the classical Feynman-Kac formulae for elliptic boundary value problems in smooth domains and with smooth coefficients which were obtained in the 1980s and 1990s using the Feller semigroup approach and Ito stochastic calculus. In contrast to this well-studied situation,…
Isometrically Homogeneous and Topologically Homogeneous Continua
2016
Based on the past study of homogeneous continua, this paper concludes that compact connected metric topological groups and isometrically homogeneous continua fall into the following three mutually disjoint classes: (1) indecomposable; (2) aposyndetic and semi-indecomposable; (3) mutually aposyndetic. Among all continua these are special classes with members having extremal properties. Indecomposable isometrically homogeneous continua are characterized as solenoids, and one-dimensional isometrically homogeneous continua are characterized as solenoids or circles. It is shown that path connected isometrically homogeneous continua are locally connected.
The 1,3-dipolar cycloaddition of 1H-pyridinium-3-olate and 1-methylpyridinium-3-olate with methyl acrylate: a density functional theory study
2010
The 1,3-dipolar cycloaddition reaction of 1-substituted pyridinium 3-olates with methyl acrylate is studied using density functional theory (DFT) method at the B3LYP/6-31G(d) level. The molecular mechanisms of the possible stereo- and regio-chemical pathways are characterized and explored. Solvent effects are also evaluated by the polarizable continuum model (PCM). Analysis of the results shows that there are relevant differences in the reaction pathways between the gas phase and with solvent. Only results in solvent phase are in accord with literature experimental results where 6-substituted 8-azabicyclo[3.2.1]oct-3-en-2-ones are formed preferentially. These polar cycloaddition reactions t…
The ALHAMBRA survey: Discovery of a faint QSO at z = 5.41
2013
[Aims]: We aim to illustrate the potentiality of the Advanced Large, Homogeneous Area, Medium-Band Redshift Astronomical (ALHAMBRA) survey to investigate the high-redshift universe through the detection of quasi stellar objects (QSOs) at redshifts higher than 5. [Methods]: We searched for QSOs candidates at high redshift by fitting an extensive library of spectral energy distributions-including active and non-active galaxy templates, as well as stars-to the photometric database of the ALHAMBRA survey (composed of 20 optical medium-band plus the 3 broad-band JHKs near-infrared filters). [Results]: Our selection over ≈1 square degree of ALHAMBRA data (∼1/4 of the total area covered by the sur…
Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and to interpret experiments
2012
Theoretical descriptions of static properties of polymer brushes are reviewed, with an emphasis on monodisperse macromolecules grafted to planar, cylindrical, or spherical substrates. Blob concepts and resulting scaling relations are outlined, and various versions of the self-consistent field theory are summarized: the classical approximation and the strong stretching limit, as well as the lattice formulation. The physical justification of various inherent assumptions is discussed, and computer simulation results addressing the test of the validity of these approximations are reviewed. Also, alternative theories, such as the single chain mean field theory and the density functional theory, …