Optimal domain of qq-concave operators and vector measure representation of qq-concave Banach lattices

Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years

Sagnac Effect of Goedel's Universe

We present exact expressions for the Sagnac effect of Goedel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Goedel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.Comment: 26 pages, including 4 figures, corrected typos, changed reference

Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal

We study the dynamics of the 2+1 Dirac oscillator exactly and find spin oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model, describing the interaction of a two-level atom with a quantized single-mode field. This equivalence allows us to map a series of quantum optical phenomena onto the relativistic oscillator, and viceversa. We make a realistic experimental proposal, at reach with current technology, for studying the equivalence of both models using a single trapped ion.Comment: Revtex4, submitted for publicatio

Human summating potential using continuous loop averaging deconvolution: Response amplitudes vary with tone burst repetition rate and duration

Electrocochleography (ECochG) to high repetition rate tone bursts may have advantages over ECochG to clicks with standard slow rates. Tone burst stimuli presented at a high repetition rate may enhance summating potential (SP) measurements by reducing neural contributions resulting from neural adaptation to high stimulus repetition rates. To allow for the analysis of the complex ECochG responses to high rates, we deconvolved responses using the Continuous Loop Averaging Deconvolution (CLAD) technique. We examined the effect of high stimulus repetition rate and stimulus duration on SP amplitude measurements made with extratympanic ECochG to tone bursts in 20 adult females with normal hearing. We used 500 and 2,000 Hz tone bursts of various stimulus durations (12, 6, 3 ms) and repetition rates (five rates ranging from 7.1 to 234.38/s). A within-subject repeated measures (rate x duration) analysis of variance was conducted. We found that, for both 500 and 2,000 Hz stimuli, the mean deconvolved SP amplitudes were larger at faster repetition rates (58.59 and 97.66/s) compared to slower repetition rates (7.1 and 19.53/s), and larger at shorter stimulus duration compared longer stimulus duration. Our concluding hypothesis is that large SP amplitude to short duration stimuli may originate primarily from neural excitation, and large SP amplitudes to long duration, fast repetition rate stimuli may originate from hair cell responses. While the hair cell or neural origins of the SP to various stimulus parameters remains to be validated, our results nevertheless provide normative data as a step toward applying the CLAD technique to understanding diseased ears

Describing Pediatric Hospital Discharge Planning Care Processes Using the Omaha System

Purpose Although discharge planning (DP) is recognized as a critical component of hospital care, national initiatives have focused on older adults, with limited focus on pediatric patients. We aimed to describe patient problems and targeted interventions as documented by social workers or DP nurses providing specialized DP services in a children\u27s hospital. Methods Text from 67 clinical notes for 28 patients was mapped to a standardized terminology (Omaha System). Data were deductively analyzed. Results A total of 517 phrases were mapped. Eleven of the 42 Omaha System problems were identified. The most frequent problem was health care supervision (297/517; 57.4%). Three Omaha System intervention categories were used (teaching, guidance, and counseling; case management; and surveillance). Intervention targets are varied by role. Conclusion The findings provide a rich description of the nature of DP for complex pediatric patients and increase our understanding of the work of DP staff and the influence of the DP practice model