On Effective Constraints for the Riemann-Lanczos System of Equations

There have been conflicting points of view concerning the Riemann--Lanczos problem in 3 and 4 dimensions. Using direct differentiation on the defining partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar (in dimensions n > 2) have argued that there are effective constraints so that not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of integrability of ideals of differential forms Bampi and Caviglia have argued that there are no such constraints in dimensions n < 5, and that, in these dimensions, all Riemann tensors can have Lanczos potentials. In this paper we give a simple direct derivation of a constraint equation, confirm explicitly that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue that the Bampi and Caviglia conclusion must therefore be flawed. In support of this, we refer to the recent work of Dolan and Gerber on the three dimensional problem; by a method closely related to that of Bampi and Caviglia, they have found an 'internal identity' which we demonstrate is precisely the three dimensional version of the effective constraint originally found by Massa and Pagani, and Edgar.Comment: 9pages, Te

Interpreting a conformally flat pure radiation space-time

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can be represented as null (half) hyperplanes rolled around a two-dimensional null cone. In the impulsive limit, the solution reduces to a pp-wave whose direction of propagation depends on retarded time. In the general case, there is a coordinate singularity which corresponds to an envelope of the wave surfaces. The global structure is discussed and a possible vacuum extension through the envelope is proposed.Comment: 9 pages, Plain TeX, 2 figures. To appear in Class. Quantum Grav. Reference adde

Three-dimensional microfabrication through a multimode optical fiber

Additive manufacturing, also known as 3D printing, is an advanced manufacturing technique that allows the fabrication of arbitrary macroscopic and microscopic objects. All 3D printing systems require large optical elements or nozzles in proximity to the built structure. This prevents their use in applications in which there is no direct access to the area where the objects have to be printed. Here, we demonstrate three-dimensional microfabrication based on two-photon polymerization (TPP) with sub diffraction-limited resolution through an ultra-thin, 50 mm long printing nozzle of 560 micrometers in diameter. Using wavefront shaping, femtosecond infrared pulses are focused and scanned through a multimode optical fiber (MMF) inside a photoresist that polymerizes via two-photon absorption. We show the construction of arbitrary 3D structures of 500 nm resolution on the other side of the fiber. To our knowledge, this is the first demonstration of microfabrication through a multimode optical fiber. Our work represents a new area which we refer to as endofabrication

Nonthermal X-Ray Emission from G266.2-1.2 (RX J0852.0-4622)

The newly discovered supernova remnant G266.2-1.2 (RX J0852.0-4622), along the line of sight to the Vela SNR, was observed with ASCA for 120 ks. We find that the X-ray spectrum is featureless, and well described by a power law, extending to three the class of shell-type SNRs dominated by nonthermal X-ray emission. Although the presence of the Vela SNR compromises our ability to accurately determine the column density, the GIS data appear to indicate absorption considerably in excess of that for Vela itself, indicating that G266.2-1.2 may be several times more distant. An unresolved central source may be an associated neutron star, though difficulties with this interpretation persist.Comment: 4 pages, 5 figures, uses aipproc.sty & epsfig.sty. To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

On the Symmetries of the Edgar-Ludwig Metric

The conformal Killing equations for the most general (non-plane wave) conformally flat pure radiation field are solved to find the conformal Killing vectors. As expected fifteen independent conformal Killing vectors exist, but in general the metric admits no Killing or homothetic vectors. However for certain special cases a one-dimensional group of homotheties or motions may exist and in one very special case, overlooked by previous investigators, a two-dimensional homethety group exists. No higher dimensional groups of motions or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure

The social learning of threat and safety in the family:Parent-to-child transmission of social fears via verbal information

Parental verbal threat (vs. safety) information regarding the social world may impact a child's fear responses, evident in subjective, behavioral, cognitive, and physiological indices of fear. In this study, primary caregivers provided standardized verbal threat or safety information to their child (N = 68, M = 5.27 years; 34 girls) regarding two strangers in the lab. Following this manipulation, children reported fear beliefs for each stranger. Physiological and behavioral reactions were recorded as children engaged with the two strangers (who were blind to their characterization) in a social interaction task. Child attention to the strangers was measured in a visual search task. Parents also reported their own, and their child's, social anxiety symptoms. Children reported more fear for the stranger paired with threat information, but no significant differences were found in observed child fear, attention, or heart rate. Higher social anxiety symptoms on the side of the parents and the children exacerbated the effect of parental verbal threat on observed fear. Our findings reveal a causal influence of parental verbal threat information only for child‐reported fear and highlight the need to further refine the conditions under which acquired fear beliefs persist and generalize to behavior/physiology or get overruled by nonaversive real‐life encounters

METHOD FOR THE PRODUCTION OF HIGH SATURATED, LOW POLYUNSATURATED SOYBEAN OIL

Methods of genetically modifying soybean plants to alter the fatty acid properties of the oil are described

Untangling Source-To-Sink Geochemical Signals in a ~3.5 Ga Martian Lake: Sedimentology and Geochemistry of the Murray Formation

Sedimentary rocks are historical archives of planetary surface processes; their grains, textures, and chemistry integrate the effects of source terrains, paleoclimatic conditions, weathering and transport processes, authigenic mineral precipitation, and diagenesis, which records groundwater chemistry through time. Source to Sink basin analysis seeks to constrain the influence of each of these different signals through sedimentary and geochemical analyses. Here, we use Mars Science Laboratory (MSL) Curiosity rover images and geochemical and mineralogical data from a traverse across a portion of the Murray formationthe lowermost unit exposed in the Gale crater central moundto begin to constrain the aspects of the source to sink system that formed this Martian mudstone between 3.7 and 3.2 Ga