Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Doitchinov's Construct of Supertopological Spaces is Topological

It is shown that the construct of supertopological spaces and continuous maps is topological.

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Embeddings of α-Modulation Spaces

2010 Mathematics Subject Classification: 42B35, 46E35.

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

On string topology of classifying spaces

Peer reviewed

On string topology of classifying spaces

Peer reviewed

On string topology of classifying spaces

Peer reviewed

Contributors to and impact of residual shunting after device closure of atrial septal defects.

BACKGROUND: The prevalence of residual shunt in patients after device closure of atrial septal defect and its impact on long-term outcome has not been previously defined. METHODS: From a prospective, single-institution registry of 408 patients, we selected individuals with agitated saline studies performed 1 year after closure. Baseline echocardiographic, invasive hemodynamic, and comorbidity data were compared to identify contributors to residual shunt. Survival was determined by review of the medical records and the Social Security Death Index. Survival analysis according to shunt included construction of Kaplan-Meier curves and Cox proportional hazards modeling. RESULTS: Among 213 analyzed patients, 27% were men and age at repair was 47 ± 17 years. Thirty patients (14%) had residual shunt at 1 year. Residual shunt was more common with Helex (22%) and CardioSEAL/STARFlex (40%) occluder devices than Amplatzer devices (9%; P = .005). Residual shunts were more common in whites (79% vs 46%, P = .004). At 7.3 ± 3.3 years of follow-up, 13 (6%) of patients had died, including 8 (5%) with Amplatzer, 5 (25%) with CardioSEAL/STARFlex, and 0 with Helex devices. Patients with residual shunting had a higher hazard of death (20% vs 4%, P = .001; hazard ratio 4.95 [1.59-14.90]). In an exploratory multivariable analysis, residual shunting, age, hypertension, coronary artery disease, and diastolic dysfunction were associated with death. CONCLUSIONS: Residual shunt after atrial septal defect device closure is common and adversely impacts long-term survival.

Energy efficiency and climate policy in the management of public spaces: public lighting

Public Lightning is an important part of municipality’s nighttime landscape. Lighting can be used to enhance public safety and security while improving the aesthetic appeal of the surrounding properties but with the current global financial crisis, such lighting systems must also be sustainable. Most climate policy efforts focus on the state and international level, however national governments won’t be able to meet their international commitments without local action. In Portugal, the Public Lighting is responsible for 3% of energy consumption. The problem is that the trend is to increase (about 4-5% per year) which represents very high costs for the municipal authorities. In terms of numbers are analyzed in this thesis 45 of 278 existent in Continental Portugal what represents only 16,2 % of the counties. This where the local authorities in Portugal that had a Sustainable Energy Action Plan (SEAP) that had been accepted and made available in the Covenant of Mayors website until the end of year 2013. It is important that the Covenant of Mayors will increase the local authorities awareness for energy efficiency and especially to public lighting because there is still a long way to go in terms of energy consumption reduction. In future works it would be interesting to see the payback of the EolGreen post in a real scenario due to lack of energy consumption from the grid it would allow to have a pretty high initial investment even with the maintenance that those technologies need.