Search results for " dimension"
showing 10 items of 881 documents
A note on topological dimension, Hausdorff measure, and rectifiability
2020
The purpose of this note is to record a consequence, for general metric spaces, of a recent result of David Bate. We prove the following fact: Let $X$ be a compact metric space of topological dimension $n$. Suppose that the $n$-dimensional Hausdorff measure of $X$, $\mathcal H^n(X)$, is finite. Suppose further that the lower n-density of the measure $\mathcal H^n$ is positive, $\mathcal H^n$-almost everywhere in $X$. Then $X$ contains an $n$-rectifiable subset of positive $\mathcal H^n$-measure. Moreover, the assumption on the lower density is unnecessary if one uses recently announced results of Cs\"ornyei-Jones.
Existence of doubling measures via generalised nested cubes
2012
Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass distribution principle lead into a simple proof for the existence of doubling measures. As an application, we show that for each $\epsilon>0$ there is a doubling measure having full measure on a set of packing dimension at most $\epsilon$.
Norm or numerical radius attaining polynomials on C(K)
2004
Abstract Let C(K, C ) be the Banach space of all complex-valued continuous functions on a compact Hausdorff space K. We study when the following statement holds: every norm attaining n-homogeneous complex polynomial on C(K, C ) attains its norm at extreme points. We prove that this property is true whenever K is a compact Hausdorff space of dimension less than or equal to one. In the case of a compact metric space a characterization is obtained. As a consequence we show that, for a scattered compact Hausdorff space K, every continuous n-homogeneous complex polynomial on C(K, C ) can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the u…
Visible parts and dimensions
2003
We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…
One-dimensional families of projections
2008
Let m and n be integers with 0 < m < n. We consider the question of how much the Hausdorff dimension of a measure may decrease under typical orthogonal projections from onto m-planes provided that the dimension of the parameter space is one. We verify the best possible lower bound for the dimension drop and illustrate the sharpness of our results by examples. The question stems naturally from the study of measures which are invariant under the geodesic flow.
The Calderón Problem for a Space-Time Fractional Parabolic Equation
2020
In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded...
Eficacia del aprendizaje servicio en dimensiones académicas, personales y sociales clave, y su incidencia en la satisfacción estudiantil en la docenc…
2017
El trabajo de investigación que se presenta se justifica por la centralidad que otorga la doctoranda a las metodologías docentes para implementar una docencia de calidad. Por ello, aun advirtiendo las dificultades, incluso las contrariedades e intereses en algunos aspectos de la unificación del EEES, el hecho de que haya considerado a las metodologías docentes innovadoras, uno de los ejes del nuevo escenario educativo europeo, se valora como una medida eficaz para la Universidad. Además, en este escenario cada vez suena con más fuerza el concepto de "desarrollo sostenible" en la Universidad y se señala a las metodologías como una de las claves para articular el modelo de educación por compe…
Medical Data Mining for Heart Diseases and the Future of Sequential Mining in Medical Field
2018
Data Mining in general is the act of extracting interesting patterns and discovering non-trivial knowledge from a large amount of data. Medical data mining can be used to understand the events happened in the past, i.e. studying a patients vital signs to understand his complications and discover why he has died, or to predict the future by analyzing the events that had happened. In this chapter we are presenting an overview on studies that use data mining to predict heart failure and heart diseases classes. We will also focus on one of the trendiest data-mining field, namely the Sequential Mining, which is a very promising paradigm. Due to its important results in many fields, this chapter …
Enthalpic and entropic contributions of water molecules to the functional T → R transition of human hemoglobin in solution
1992
Generalized solvent-mediated forces contribute to free energy at the functional T → R transition of human hemoglobin A (HbA). Their contribution is here sorted out quantitatively in both its enthalpic and entropic parts, along with the average number of water molecules involved. The latter (about 75 waters in average) must be considered together with HbA as one statistically defined functional unit for oxygen transport. Their configurations are expected to undergo frequent structural rearrangements. Lifetimes of statistically relevant configurations do not need to (although, of course, they may) exceed by more than a factor 5 the normal H-bond lifetimes of the pure solvent. Compared to the …
Argumentativeness and political participation: A cross-cultural analysis in the United States and Turkey
2013
This study is an examination of the relationship between argumentativeness and political participation and the moderating effect of nationality on this relationship. Through a survey analysis of 801 individuals in the United States (592) and Turkey (209), the following was found: Americans are more argumentative than Turks, Turks participate more in politics than Americans, argumentativeness and political participation are not significantly correlated, and nationality does not significantly affect the relationship between argumentativeness and political participation. Cultural differences between the United States and Turkey are discussed as reasons for differences between the two nations i…