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]).

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

Law Enforcement Actions in Urban Spaces Governed by Violent Non-State Entities: Lessons from Latin America

In response to a crime epidemic afflicting Latin America since the early 1990s, several countries in the region have resorted to using heavy-force police or military units to physically retake territories de facto controlled by non-State criminal or insurgent groups. After a period of territory control, the heavy forces hand law enforcement functions in the retaken territories to regular police officers, with the hope that the territories and their populations will remain under the control of the state. To a varying degree, intensity, and consistency, Brazil, Colombia, Mexico, and Jamaica have adopted such policies since the mid-1990s. During such operations, governments need to pursue two interrelated objectives: to better establish the state’s physical presence and to realign the allegiance of the population in those areas toward the state and away from the non-State criminal entities. From the perspective of law enforcement, such operations entail several critical decisions and junctions, such as: Whether or not to announce the force insertion in advance. The decision trades off the element of surprise and the ability to capture key leaders of the criminal organizations against the ability to minimize civilian casualties and force levels. The latter, however, may allow criminals to go to ground and escape capture. Governments thus must decide whether they merely seek to displace criminal groups to other areas or maximize their decapitation capacity. Intelligence flows rarely come from the population. Often, rival criminal groups are the best source of intelligence. However, cooperation between the State and such groups that goes beyond using vetted intelligence provided by the groups, such as a State tolerance for militias, compromises the rule-of-law integrity of the State and ultimately can eviscerate even public safety gains. Sustaining security after initial clearing operations is at times even more challenging than conducting the initial operations. Although unlike the heavy forces, traditional police forces, especially if designed as community police, have the capacity to develop trust of the community and ultimately focus on crime prevention, developing such trust often takes a long time. To develop the community’s trust, regular police forces need to conduct frequent on-foot patrols with intensive nonthreatening interactions with the population and minimize the use of force. Moreover, sufficiently robust patrol units need to be placed in designated beats for substantial amount of time, often at least over a year. Establishing oversight mechanisms, including joint police-citizens’ boards, further facilities building trust in the police among the community. After disruption of the established criminal order, street crime often significantly rises and both the heavy-force and community-police units often struggle to contain it. The increase in street crime alienates the population of the retaken territory from the State. Thus developing a capacity to address street crime is critical. Moreover, the community police units tend to be vulnerable (especially initially) to efforts by displaced criminals to reoccupy the cleared territories. Losing a cleared territory back to criminal groups is extremely costly in terms of losing any established trust and being able to recover it. Rather than operating on a priori determined handover schedule, a careful assessment of the relative strength of regular police and criminal groups post-clearing operations is likely to be a better guide for timing the handover from heavy forces to regular police units. Cleared territories often experience not only a peace dividend, but also a peace deficit – in the rise new serious crime (in addition to street crime). Newly – valuable land and other previously-inaccessible resources can lead to land speculation and forced displacement; various other forms of new crime can also significantly rise. Community police forces often struggle to cope with such crime, especially as it is frequently linked to legal business. Such new crime often receives little to no attention in the design of the operations to retake territories from criminal groups. But without developing an effective response to such new crime, the public safety gains of the clearing operations can be altogether lost.

Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

Peer reviewed

Cultivating Subjectivities: The Class Politics of Convivial Labor in the Interstitial Spaces of Neoliberal Neglect

Thesis (Ph.D.)--University of Washington, 2016-08

What happens at the gap between knowledge and practice? Spaces of encounter and misencounter between environmental scientists and local people

Researchers studying processes of global environmental change are increasingly interested in their work having impacts that go beyond academia to influence policy and management. Recent scholarship in the conservation sciences has pointed to the existence of a research-action gap and has proposed various solutions for overcoming it. However, most of these studies have been limited to the spaces of dissemination, where the science has already been done and is then to be passed over to users of the information. Much less attention has been paid to encounters that occur between scientists and nonscientists during the practice of doing scientific research, especially in situations that include everyday roles of labor and styles of communication (i.e., fieldwork). This paper builds on theories of contact that have examined encounters and relations between different groups and cultures in diverse settings. I use quantitative and qualitative evidence from Madidi National Park, Bolivia, including an analysis of past research in the protected area, as well as interviews (N = 137) and workshops and focus groups (N = 12) with local inhabitants, scientists, and park guards. The study demonstrates the significance of currently unacknowledged or undervalued components of the research-action gap, such as power, respect, and recognition, to develop a relational and reciprocal notion of impact. I explain why, within such spaces of encounter or misencounter between scientists and local people, knowledge can be exchanged or hidden away, worldviews can be expanded or further entrenched, and scientific research can be welcomed or rejected.

Spectral synthesis and topologies on ideal spaces for Banach *-algebras

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G).

N=4 supersymmetric AdS(5) vacua and their moduli spaces

We classify the N = 4 supersymmetric AdS(5) backgrounds that arise as solutions of five-dimensional N = 4 gauged supergravity. We express our results in terms of the allowed embedding tensor components and identify the structure of the associated gauge groups. We show that the moduli space of these AdS vacua is of the form SU(1, m)/ (U(1) x SU(m)) and discuss our results regarding holographically dual N = 2 SCFTs and their conformal manifolds.

Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules

MSC 19L41; 55S10.