Search results for "Product topology"
showing 10 items of 14 documents
Operators on PIP-Spaces and Indexed PIP-Spaces
2009
As already mentioned, the basic idea of pip-spaces is that vectors should not be considered individually, but only in terms of the subspaces V r (r Є F), the building blocks of the structure. Correspondingly, an operator on a pipspace should be defined in terms of assaying subspaces only, with the proviso that only continuous or bounded operators are allowed. Thus an operator is a coherent collection of continuous operators. We recall that in a nondegenerate pip-space, every assaying subspace V r carries its Mackey topology \(\tau (V_r , V \bar{r})\) and thus its dual is \(V \bar{r}\). This applies in particular to \(V^{\#}\) and V itself. For simplicity, a continuous linear map between two…
On linear extension operators from growths of compactifications of products
1996
Abstract We obtain some results on product spaces. Among them we prove that for noncompact spaces X 1 and X 2 , the norm of every linear extension operator from C ( β ( X 1 × X 2 ) β ( X 1 × X 2 )) into C ( β ( X 1 × X 2 )) is greater or equal than 2, and also that β ( X 1 × X 2 ) β ( X 1 × X 2 ) is not a neighborhood retract of β ( X 1 × X 2 ).
Sets of Efficiency in a Normed Space and Inner Product
1987
In a normed space X the distances to the points of a given set A being considered as the objective functions of a multicriteria optimization problem, we define four sets of efficiency (efficient, strictly efficient, weakly efficient and properly efficient points). Instead of studying properties of the sets of efficiency according to properties of the norm, we investigate an inverse problem: deduce properties of the norm of X from properties of the sets of efficiency, valid for every finite subset A of X.
Probability Measures on Product Spaces
2020
In order to model a random time evolution, the canonical procedure is to construct probability measures on product spaces. Roughly speaking, the first step is to take a probability measure that models the initial distribution. In the second step, on a different probability space, the distribution after one time step is modeled. Then in each subsequent step, on a further probability space, the random state in the next time step given the full history is modeled. On a formal level, we consider products of probability spaces and Markov kernels between such spaces. Finally, the Ionescu-Tulcea theorem shows that the whole procedure can be realized on a single infinite product space. Furthermore,…
Comparison of canonical variate analysis and principal component analysis on 422 descriptive sensory studies
2015
International audience; Although Principal Component Analysis (PCA) of product mean scores is most often used to generate a product map from sensory profiling data, it does not take into account variance of product mean scores due to individual variability. Canonical Variate Analysis (CVA) of the product effect in the two-way (product and subject) multivariate ANOVA model is the natural extension of the classical univariate approach consisting of ANOVAs of every attribute. CVA generates successive components maximizing the ANOVA F-criterion. Thus, CVA is theoretically more adapted than PCA to represent sensory data. However, CVA requires a matrix inversion which can result in computing inst…
Large data scattering for NLKG on waveguide ℝd × 𝕋
2020
We consider the pure-power defocusing nonlinear Klein–Gordon equation, in the [Formula: see text]-subcritical case, posed on the product space [Formula: see text], where [Formula: see text] is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space [Formula: see text] for [Formula: see text]. The strategy consists in proving a suitable profile decomposition theorem on the whole manifold to pursue a concentration-compactness and rigidity method along with the proofs of (global in time) Strichartz estimates.
Linear extension operators on products of compact spaces
2003
Abstract Let X and Y be the Alexandroff compactifications of the locally compact spaces X and Y , respectively. Denote by Σ( X × Y ) the space of all linear extension operators from C(( X × Y )⧹(X×Y)) to C(( X × Y )) . We prove that X and Y are σ -compact spaces if and only if there exists a T∈Σ( X × Y ) with ‖ T ‖ Γ∈Σ( X × Y ) with ‖ Γ ‖=1. Assuming the existence of a T∈Σ( X × Y ) with ‖ T ‖ X and Y is equivalent to the fact that ‖ Γ ‖⩾2 for every Γ∈Σ( X × Y ) .
Retractive product spaces
1990
Abstract A completely regular Hausdorff space X is called retractive if there is a retraction from βX onto βX \ X . A product space is retractive if and only if all factors are compact but one which is retractive.
Generalized F-Contractions on Product of Metric Spaces
2019
Our purpose in this paper is to extend the fixed point results of a &psi
Adequate number of consumers in a liking test. Insights from resampling in seven studies
2014
The recommended number of consumers to be enrolled in a hedonic test comparing several products usually ranges from 50 to 100, at least if no liking segmentation is sought. This paper seeks to examine whether such a panel size range is adequate, by means of 7 trials with different levels of product space complexity. Five types of products were tested: Two varied in fattiness and sweetness and were tested under the same conditions in two separate laboratories (4 trials); the remaining three, varying in taste and texture, were each tested in a different laboratory (3 trials). Each of the 7 trials was run by a different laboratory. Each of the seven laboratories enrolled in its trial 150 consu…