Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

Regional actorness and interregional relations:ASEAN, the EU and Mercosur

The European Union (EU) has a long tradition of interregional dialogue mechanisms with other regional organisations and is using these relations to project its own model of institutionalised actorness. This is partly motivated by the emerging actorness of the EU itself, which benefits from fostering capable regional counterparts in other parts of the world. This article advances the argument that actorness, which we conceptualise in terms of institutions, recognition and identity, is a relational concept, dependent on context and perception. Taking the Association of Southeast Asian Nations (ASEAN) and the Common Market of the South (Mercosur) and their relations with the EU as case studies, this article demonstrates that the actorness capabilities of all three organisations have been enhanced as result of ASEAN-EU and Mercosur-EU relations. However, there are clear limits to the development of the three components of regional actorness and to the interregional relations themselves. These limits stem both from the type of interregionalism at play and from the different regional models the actors incorporate. While there is evidence of institutional enhancement in ASEAN and Mercosur, these formal changes have been grafted on top of firmly entrenched normative underpinnings. Within the regional organisations, interactions with the EU generate centrifugal forces concerning the model to pursue, thus limiting their institutional cohesion and capacity. In addition, group-to-group relations have reinforced ASEAN and Mercosur identities in contrast to the EU. The formation of such differences has narrowed the scope of EU interregionalism despite the initial success of improved regional actorness

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Microlensing discovery of a population of very tight, very low mass binary brown dwarfs

Although many models have been proposed, the physical mechanisms responsible for the formation of low-mass brown dwarfs (BDs) are poorly understood. The multiplicity properties and minimum mass of the BD mass function provide critical empirical diagnostics of these mechanisms. We present the discovery via gravitational microlensing of two very low mass, very tight binary systems. These binaries have directly and precisely measured total system masses of 0.025 M [SUB]⊙[/SUB] and 0.034 M [SUB]⊙[/SUB], and projected separations of 0.31 AU and 0.19 AU, making them the lowest-mass and tightest field BD binaries known. The discovery of a population of such binaries indicates that BD binaries can robustly form at least down to masses of ~0.02 M [SUB]⊙[/SUB]. Future microlensing surveys will measure a mass-selected sample of BD binary systems, which can then be directly compared to similar samples of stellar binaries

Genome-Wide Mutagenesis of Xanthomonas axonopodis pv. citri Reveals Novel Genetic Determinants and Regulation Mechanisms of Biofilm Formation

Xanthomonas axonopodis pv. citri (Xac) causes citrus canker disease, a major threat to citrus production worldwide. Accumulating evidence suggests that the formation of biofilms on citrus leaves plays an important role in the epiphytic survival of this pathogen prior to the development of canker disease. However, the process of Xac biofilm formation is poorly understood. Here, we report a genome-scale study of Xac biofilm formation in which we identified 92 genes, including 33 novel genes involved in biofilm formation and 7 previously characterized genes, colR, fhaB, fliC, galU, gumD, wxacO, and rbfC, known to be important for Xac biofilm formation. In addition, 52 other genes with defined or putative functions in biofilm formation were identified, even though they had not previously reported been to be associated with biofilm formation. The 92 genes were isolated from 292 biofilm-defective mutants following a screen of a transposon insertion library containing 22,000 Xac strain 306 mutants. Further analyses indicated that 16 of the novel genes are involved in the production of extracellular polysaccharide (EPS) and/or lipopolysaccharide (LPS), 7 genes are involved in signaling and regulatory pathways, and 5 genes have unknown roles in biofilm formation. Furthermore, two novel genes, XAC0482, encoding a haloacid dehalogenase-like phosphatase, and XAC0494 (designated as rbfS), encoding a two-component sensor protein, were confirmed to be biofilm-related genes through complementation assays. Our data demonstrate that the formation of mature biofilm requires EPS, LPS, both flagellum-dependent and flagellum-independent cell motility, secreted proteins and extracellular DNA. Additionally, multiple signaling pathways are involved in Xac biofilm formation. This work is the first report on a genome-wide scale of the genetic processes of biofilm formation in plant pathogenic bacteria. The report provides significant new information about the genetic determinants and regulatory mechanism of biofilm formation

Microlensig Binaries with Candidate Brown Dwarf Companions

Brown dwarfs are important objects because they may provide a missing link between stars and planets, two populations that have dramatically different formation history. In this paper, we present the candidate binaries with brown dwarf companions that are found by analyzing binary microlensing events discovered during 2004 - 2011 observation seasons. Based on the low mass ratio criterion of q < 0.2, we found 7 candidate events, including OGLE-2004-BLG-035, OGLE-2004-BLG-039, OGLE-2007-BLG-006, OGLE-2007-BLG-399/MOA-2007-BLG-334, MOA-2011-BLG-104/OGLE-2011-BLG-0172, MOA-2011-BLG-149, and MOA-201-BLG-278/OGLE-2011-BLG-012N. Among them, we are able to confirm that the companions of the lenses of MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149 are brown dwarfs by determining the mass of the lens based on the simultaneous measurement of the Einstein radius and the lens parallax. The measured mass of the brown dwarf companions are (0.02 +/- 0.01) M_Sun and (0.019 +/- 0.002) M_Sun for MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149, respectively, and both companions are orbiting low mass M dwarf host stars. More microlensing brown dwarfs are expected to be detected as the number of lensing events with well covered light curves increases with new generation searches.Comment: 10 pages, 9 figures, 4 table