An abstract version of the concentration compactness principle

We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains.We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains

Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical systems

We consider a conservative ergodic measure-preserving transformation T of a σ-finite measure space (X,B,μ) with μ(X)=∞. Given an observable f:X→ℝ we study the almost sure asymptotic behaviour of the Birkhoff sums S_Nf(x). In infinite ergodic theory it is well known that the asymptotic behaviour of SNf(x) strongly depends on the point x∈X, and if f∈L^1(X,μ), then there exists no real valued sequence (b(N)) such that lim S_Nf(x)/b(N)=1 almost surely. In this paper we show that for dynamical systems with strong mixing assumptions for the induced map on a finite measure set, there exists a sequence (α(N)) and m:X×ℕ→ℕ such that for f∈L^1(X,μ) we have lim S_{N+m(x,N)}f(x)/α(N)=1 for μ-a.e. x∈X. Moreover if f∉L1(X,μ) we give conditions on the induced observable such that there exists a sequence (G(N)) depending on f, for which lim S_Nf(x)/G(N)=1 holds for μ-a.e. x∈X

The effect of partner-directed emotion in social exchange decision-making

Despite the prevalence of studies examining economic decision-making as a purely rational phenomenon, common sense suggests that emotions affect our decision-making particularly in a social context. To explore the influence of emotions on economic decision-making, we manipulated opponent-directed emotions prior to engaging participants in two social exchange decision-making games (the Trust Game and the Prisoner's Dilemma). Participants played both games with three different (fictional) partners and their tendency to defect was measured. Prior to playing each game, participants exchanged handwritten “essays” with their partners, and subsequently exchanged evaluations of each essay. The essays and evaluations, read by the participant, were designed to induce either anger, sympathy, or a neutral emotional response toward the confederate with whom they would then play the social exchange games. Galvanic skin conductance level (SCL) showed enhanced physiological arousal during anger induction compared to both the neutral and sympathy conditions. In both social exchange games, participants were most likely to defect against their partner after anger induction and least likely to defect after sympathy induction, with the neutral condition eliciting intermediate defection rates. This pattern was found to be strongest in participants exhibiting low cognitive control (as measured by a Go/no-Go task). The findings indicate that emotions felt toward another individual alter how one chooses to interact with them, and that this influence depends both on the specific emotion induced and the cognitive control of the individual

Low-T_c Josephson junctions with tailored barrier

Nb/Al_2O_3/Ni_{0.6}Cu_{0.4}/Nb based superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson tunnel junctions with a thickness step in the metallic ferromagnetic \Ni_{0.6}\Cu_{0.4} interlayer were fabricated. The step was defined by optical lithography and controlled etching. The step height is on the scale of a few angstroms. Experimentally determined junction parameters by current-voltage characteristics and Fraunhofer pattern indicate an uniform F-layer thickness and the same interface transparencies for etched and non-etched F-layers. This technique could be used to tailor low-T_c Josephson junctions having controlled critical current densities at defined parts of the junction area, as needed for tunable resonators, magnetic-field driven electronics or phase modulated devices.Comment: 6 pages, 6 figures, small changes, to be published by JA

Magellan Spectroscopy of the Galaxy Cluster RX J1347.5-1145: Redshift Estimates for the Gravitationally Lensed Arcs

We present imaging and spectroscopic observations of the gravitationally lensed arcs in the field of RX J1347.5-1145, the most X-ray luminous galaxy cluster known. Based on the detection of the [OII] 3727 emission line, we confirm that the redshift of one of the arcs is z = 0.806. Its color and [OII] line strength are consistent with those of distant, actively star forming galaxies. In a second arc, we tentatively identify a pair of absorption lines superposed on a red continuum; the lines are consistent with Ca II H & K at z = 0.785. We detected a faint blue continuum in two additional arcs, but no spectral line features could be measured. We establish lower limits to their redshifts based on the absence of [OII] emission, which we argue should be present and detectable in these objects. Redshifts are also given for a number of galaxies in the field of the cluster.Comment: To appear in The Astrophysical Journal (September 2002). 6 page

Implications of surface noise for the motional coherence of trapped ions

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$\mu$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both, the observed heating as well as the measured dephasing, satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.Comment: (5 pages, 4 figures

Lay conceptions of “being moved” (“bewegt sein”) include a joyful and a sad type: Implications for theory and research

Being moved has received increased attention in emotion psychology as a social emotion that fosters bonds between individuals and within communities. This increased attention, however, has also sparked debates about whether the term “being moved” refers to a single distinct profile of emotion components or rather to a range of different emotion profiles. We addressed this question by investigating lay conceptions of the emotion components (i.e., elicitors, cognitive appraisals, subjective feelings, bodily symptoms, and consequences for thought/action) of “bewegt sein” (the German term for “being moved”). Participants (N = 106) provided written descriptions of both a moving personal experience and their conceptual prototype of “being moved,” which were subjected to content analysis to obtain quantitative data for statistical analyses. Based on latent class analyses, we identified two classes for both the personal experiences (joyfully-moved and sadly-moved classes) and the being-moved prototype (basic-description and extended-description classes). Being joyfully moved occurred when social values and positive relationship experiences were salient. Being sadly moved was elicited by predominantly negative relationship experiences and negatively salient social values. For both classes, the most frequently reported consequences for thought/action were continued cognitive engagement, finding meaning, and increased valuation of and striving for connectedness/prosociality. Basic descriptions of the prototype included “being moved” by positive or negative events as instances of the same emotion, with participants in the extended-description class also reporting joy and sadness as associated emotions. Based on our findings and additional theoretical considerations, we propose that the term “being moved” designates an emotion with an overall positive valence that typically includes blends of positively and negatively valenced emotion components, in which especially the weight of the negative components varies. The emotion’s unifying core is that it involves feeling the importance of individuals, social entities, and abstract social values as sources of meaning in one’s life

Hosting the plant cells in vitro : recent trends in bioreactors

Biotechnological production of high-value metabolites and therapeutic proteins by plant in vitro systems has been considered as an attractive alternative of classical technologies. Numerous proof-of-concept studies have illustrated the feasibility of scaling up plant in vitro system-based processes while keeping their biosynthetic potential. Moreover, several commercial processes have been established so far. Though the progress on the field is still limited, in the recent years several bioreactor configurations has been developed (e.g., so-called single-use bioreactors) and successfully adapted for growing plant cells in vitro. This review highlights recent progress and limitations in the bioreactors for plant cells and outlines future perspectives for wider industrialization of plant in vitro systems as “green cell factories” for sustainable production of value-added molecules

Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots

We have studied the monolayer-bilayer transformation in the case of the coherent Stranski-Krastanov growth. We have found that the energy of formation of a second layer nucleus is largest at the center of the first-layer island and smallest on its corners. Thus nucleation is expected to take place at the corners (or the edges) rather than at the center of the islands as in the case of homoepitaxy. The critical nuclei have one atom in addition to a compact shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with i>1 an integer. When the edge of the initial monolayer island is much larger than the critical nucleus size, the latter is always a rectangle plus an additional atom, adsorbed at the longer edge, which gives rise to a new atomic row in order to transform the rectangle into the equilibrium square shape.Comment: 6 pages, 4 figures. Accepted version, minor change

Concentration analysis and cocompactness

Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach spaces, $X\hookrightarrow Y$, and $D$ is, typically, a set of surjective isometries on both $X$ and $Y$. A profile decomposition is a representation of a bounded sequence in $X$ as a sum of elementary concentrations of the form $g_kw$, $g_k\in D$, $w\in X$, and a remainder that vanishes in $Y$. A necessary requirement for $Y$ is, therefore, that any sequence in $X$ that develops no $D$-concentrations has a subsequence convergent in the norm of $Y$. An imbedding $X\hookrightarrow Y$ with this property is called $D$-cocompact, a property weaker than, but related to, compactness. We survey known cocompact imbeddings and their role in profile decompositions