Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n, n) for any n ≥ 3. These examples admit a natural almost para-Hermitian structure and are semi para-complex Osserman with non-trivial Jordan normal form as well; they neither satisfy the third Gray identity nor are they integrable.     

The local index density of the perturbed de Rham complex

Czechoslovak Mathematical Journal - A perturbation of the de Rham complex was introduced by Witten for an exact 1-form Θ and later extended by Novikov for a closed 1-form on a Riemannian...     

Homogeneous 4-Dimensional Kähler–Weyl Structures

Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kähler–Weyl structure; this structure is locally conformally Kähler if and only if the alternating Ricci tensor ρ _a vanishes. The tensor ρ _a takes values in a certain representation space. In this paper, we show that any algebraic possibility Ξ in this representation space can in fact be geometrically realized by a left-invariant Kähler–Weyl structure on a 4-dimensional Lie group in either the Hermitian or the para-Hermitian setting.     

Neumann heat content asymptotics with singular initial temperature and singular specific heat

We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail as are recursion relations among the coefficients and the relationship between the Dirichlet and Robin settings.     

Binaural detection with narrowband and wideband reproducible noise maskers. III. Monaural and diotic detection and model results

A single-interval, yes-no, tone-in-noise detection experiment was conducted to measure the proportion of "tone present" responses to each of 25 reproducible noise-alone and tone-plus-noise waveforms under narrowband (100 Hz), wideband (2900 Hz), monotic, and diotic stimulus conditions. Proportions of "tone present" responses (estimates of the probabilities of hits and false alarms) were correlated across masker bandwidths and across monotic and diotic conditions. Two categories of models were considered; one based on stimulus energy or neural counts, and another based on temporal structure of the stimulus envelope or neural patterns. Both categories gave significant correlation between decision variables and data. A model based on a weighted combination of energy in multiple critical bands performed best, predicting up to 90% of the variance in the reproducible-noise data. However, since energy-based models are unable to successfully explain detection under a roving-level paradigm without substantial modification, it is argued that other variations of detection models must be considered for future study. Temporal models are resistant to changes in threshold under roving-level conditions, but explained at most only 67% of the variance in the reproducible-noise data.     

Universal curvature identities II

We show that any universal curvature identity which holds in the Riemannian setting extends naturally to the pseudo-Riemannian setting. Thus the Euh-Park-Sekigawa identity also holds for pseudo-Riemannian manifolds. We study the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and show that as in the Riemannian setting, they are given solely in terms of curvature (and not in terms of covariant derivatives of curvature) even in the pseudo-Riemannian setting.     

The eta invariant and metrics of positive scalar curvature

Research partially supported by the NSF     

Electron Microscopy of Rhamnolipid (Biosurfactant) Morphology: Effects of pH, Cadmium, and Octadecane

A rhamnolipid biosurfactant produced by Pseudomonas aeruginosa ATCC 9027 is reported to increase the aqueous dispersion and biodegradation of petroleum hydrocarbons and to complex heavy metals. These reports indicate the potential for application of rhamnolipids in remediation of contaminated sites. Effective use of rhamnolipids will require understanding of rhamnolipid morphology and the effects of pH and organic and inorganic contaminants on that morphology. We used cryo-transmission electron microscopy to investigate the morphology of vitrified, frozen hydrated suspensions of rhamnolipid over a pH range of 5.5 to 8.0, and to determine the effect of a model alkane, octadecane, and a model heavy metal, cadmium, on rhamnolipid morphology. Micrographs clearly showed that rhamnolipid morphology was a function of pH, changing from lamellar, to vesicular, to micellar as pH increased. The effect of cadmium and octadecane on rhamnolipid morphology was determined at pH 6.8 and 7.0, where maximum cadmium complexation and maximum octadecane dispersion occurs. Cadmium seemed to stabilize rhamnolipid vesicle structures as shown by an increase in vesicle number and a decrease in vesicle diameter. In contrast, octadecane favored the micellar structure as shown by the complete absence of vesicles.