Search results for "vector space"
showing 10 items of 287 documents
On singular integral and martingale transforms
2007
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.
Group topologies coarser than the Isbell topology
2011
Abstract The Isbell, compact-open and point-open topologies on the set C ( X , R ) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α ( X ) of compact families of open subsets of a topological space X . Those α ( X ) for which addition is jointly continuous at the zero function in C α ( X , R ) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α ( X ) for which C α ( X , R ) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, t…
Predicting the Short-Term Exchange Rate Between United State Dollar and Czech Koruna Using Hilbert-Huang Transform and Fuzzy Logic
2017
In this paper, the combination of the Hilbert-Huang Transform, fuzzy logic and an embedding theorem is described to predict the short-term exchange rate from United States dollar to Czech Koruna. By Using the Hilbert-Huang Transform as an adaptive filter, the proposed method decreases the embedding dimension space from five (original samples) to four (de-noising samples). This dimension space provides the number of inputs to the fuzzy rule base system, which causes the number of rules, the time for training and the inference process to decrease. Experimental results indicated that this method achieves higher accuracy prediction than the direct use of original data.
Nonlinear analysis of continuous ECG during sleep I. Reconstruction.
2000
In recent years evidence has accumulated that ECG signals are of a nonlinear nature. It has been recognized that strictly periodic cardiac rhythms are not accompanied by healthy conditions but, on the contrary, by pathological states. Therefore, the application of methods from nonlinear system theory for the analysis of ECG signals has gained increasing interest. Crucial for the application of nonlinear methods is the reconstruction (embedding) of the time series in a phase space with appropriate dimension. In this study continuous ECG signals of 12 healthy subjects recorded during different sleep stages were analysed. Proper embedding dimension was determined by application of two techniqu…
Individual differences in working memory capacity are unrelated to the magnitudes of retrocue benefits
2021
AbstractPrevious studies have associated visual working memory (VWM) capacity with the use of internal attention. Retrocues, which direct internal attention to a particular object or feature dimension, can improve VWM performance (i.e., retrocue benefit, RCB). However, so far, no study has investigated the relationship between VWM capacity and the magnitudes of RCBs obtained from object-based and dimension-based retrocues. The present study explored individual differences in the magnitudes of object- and dimension-based RCBs and their relationships with VWM capacity. Participants completed a VWM capacity measurement, an object-based cue task, and a dimension-based cue task. We confirmed tha…
Association between nutritional values of hays fed to horses and sensory properties as perceived by human sight, touch and smell
2019
International audience; Although hay is the foundation of most equine diets, horse owners rarely ask for biochemical analysis and the routine practice is to choose hay based on its 'perceived' nutritional value. The present study aimed at exploring the relationship between sensory properties as perceived by sight, touch and smell, and the nutritional value of hay measured by biochemical analysis using a 'free sorting task' method. Fifty-four non-expert participants were asked individually to: (1) observe 21 hays samples, (2) group together hays that they perceived as similar for each of the three modalities (hay appearance, odour or texture) and (3) characterize each formed group with a max…
A note on the rational canonical form of an endomorphism of a vector space of finite dimension
2018
[EN] In this note, we give an easy algorithm to construct the rational canonical form of a square matrix or an endomorphism h of a finite dimensional vector space which does not depend on either the structure theorem for finitely generated modules over principal ideal domains or matrices over the polynomial ring. The algorithm is based on the construction of an element whose minimum polynomial coincides with the minimum polynomial of the endomorphism and on the fact that the h-invariant subspace generated by such an element admits an h-invariant complement. It is also shown that this element can be easily obtained without the factorisation of a polynomial as a product of irreducible polynom…
On some Translation Planes Admitting a Frobenius Group of Collineations
1983
Publisher Summary This chapter presents some results concerning translation planes of dimension 2 over GF(q), where q = p r . π denotes such a plane. It is assumed that π has a collineation group F of order q 2 (q-1) satisfying the condition: there exists a point V e l ∞ such that F fixes V and acts (faithfully) as a Frobenius group on l ∞ – {V}.
Fixed point spaces, primitive character degrees and conjugacy class sizes
2006
Let G be a finite group that acts on a nonzero finite dimensional vector space V over an arbitrary field. Assume that V is completely reducible as a G-module, and that G fixes no nonzero vector of V. We show that some element g ∈ G has a small fixed-point space in V. Specifically, we prove that we can choose g so that dim C V (g) < (1/p)dim V, where p is the smallest prime divisor of |G|.
On the group of the automorphisms of some algebraic systems
1968
Within a framework of general algebra we firstly formulate a proposition on the group of the automorphisms of some irreducible algebrae (id est algebrae without proper non trivial subalgebrae). This proposition includes as particular cases the uniqueness of the automorphisms of the rational field and the Burnside theorem on the commutant of an irreducible set of operators of a finite dimensional vector space over an algebraically closed field. Afterwards we apply the general proposition to modules with irreducible sets of semilinear operators and we obtain a theorem which generalises from several points of view the Burnside theorem. Finally we derive as an application a proposition which sp…