The Lanczos potential for Weyl-candidate tensors exists only in four dimensions

We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L_abc and W_abcd, then this system's integrability conditions should be checked; and so on. When we find a non-trivial condition involving only W_abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200

Interplay between the Reactions to Light and to Gravity in Phycomyces

Sporangiophores of Phycomyces do not grow directly towards a horizontal beam of light, but equilibrate at an angle of about 30° above the horizontal. After describing several related observations, this paper suggests that the dioptric properties of an obliquely illuminated cylindrical lens, illustrated by a dummy cell, as well as a negative geotropic response, play major roles in determining the direction of growth. The shift of the equilibrium direction of growth towards the vertical, or a purely geotropic response, over a tenfold range of very low intensities (around 10^6 quanta/cm^2 sec., or 10^-13 watt/cm^2) has been studied, and an action spectrum made, measuring the quantum fluxes producing a standard intermediate equilibrium direction of growth at different wavelengths. This may differ from the action spectra at higher intensities in lacking conspicuous maxima from 370 to 490 mµ. However, in the ultraviolet it parallels the other spectra, although without showing the much higher quantum efficiency of ultraviolet relative to visible light previously noted. Possible interpretations are discussed

Visual Communications on the Road in Arkansas: Analysis of Secondary Students Videos

In the summer of 2010, the Visual Communications on the Road in Arkansas: Creative Photo and Video Projects to Promote Agriculture program was initiated. The program consisted of a two-week agricultural communications curriculum that would be taught by agricultural science teachers in Arkansas. The curriculum was composed of lessons about photography, writing, and videography, and the program introduced students to digital photography and videography equipment and the proper uses of equipment. Once the curriculum was taught in secondary schools, a mobile classroom unit—consisting of a travel trailer, photography and videography equipment, and laptop computers equipped with editing software—would visit the school to assist students with the creation of short promotional videos about agriculture. The student-created videos were used as a hands-on extension of the curriculum learned in the classroom. Completed videos were posted to YouTube and then analyzed to assess student application of competencies taught in the curriculum. The researchers created a coding sheet to systematically assess all posted videos and inter- and intrarater reliability was maintained. An analysis of data gathered from the video assessment showed that secondary students were able to effectively apply many of the techniques taught in the curriculum through the agricultural videos created. Additional findings and recommendations for application and future research are presented

Awareness, use, and perceptions of biodiesel: A comparison of consumers in Belgium and the United States

Belgian (N = 61) and American (N = 134) fuel consumers were interviewed in the summer of 2012 to determine their awareness, use, and perceptions of biodiesel. Consumers who were aware of biodiesel were asked their perceptions. A significantly P \u3c 0.0001) higher percentage of Belgian consumers (78.7%) reported owning or driving a diesel vehicle compared to American consumers (9.0%). Belgian and American consumers moderately agreed biodiesel is a high-quality fuel. For both Belgian and American consumers, there was no significant association between owning a diesel vehicle and being aware of biodiesel or having purchased biodiesel. Although Belgian and American consumers agreed that using non-food crops for biodiesel is justified, Belgians were significantly less supportive than American consumers of using food crops for biodiesel. Both Belgian and American consumers disagreed with the statement “I would never use biodiesel”, and the two sets of consumers moderately disagreed that diesel engines would not run properly on biodiesel. Belgian and American consumers agreed that global warming is increasing; however, American consumers were more positive about the potential of biodiesel to reduce harmful exhaust emissions and global warming. Belgian consumers moderately agreed and American consumers agreed that biodiesel is better to use because it is made from renewable resources. Belgian and American consumers generally show similar perceptions of biodiesel, with the exception that American consumers were more positive toward the environmental and renewable aspects of biodiesel use. Recommendations for further research include gaining a better understanding of the potential positive influences that impact consumers’ perceptions of biodiesel

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

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

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

Irreducible Killing Tensors from Third Rank Killing-Yano Tensors

We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducible and two irreducible.Comment: 10 page

A user evaluation of hierarchical phrase browsing

Phrase browsing interfaces based on hierarchies of phrases extracted automatically from document collections offer a useful compromise between automatic full-text searching and manually-created subject indexes. The literature contains descriptions of such systems that many find compelling and persuasive. However, evaluation studies have either been anecdotal, or focused on objective measures of the quality of automatically-extracted index terms, or restricted to questions of computational efficiency and feasibility. This paper reports on an empirical, controlled user study that compares hierarchical phrase browsing with full-text searching over a range of information seeking tasks. Users found the results located via phrase browsing to be relevant and useful but preferred keyword searching for certain types of queries. Users experiences were marred by interface details, including inconsistencies between the phrase browser and the surrounding digital library interface

The Vertical Structure of Planet-induced Gaps in Proto-Planetary Discs

Giant planets embedded in circumstellar discs are expected to open gaps in these discs. We examine the vertical structure of the gap edges. We find that the planet excites spiral arms with significant (Mach number of a half) vertical motion of the gas, and discuss the implications of these motions. In particular, the spiral arms will induce strong vertical stirring of the dust, making the edge appeared `puffed up' relative to the bulk of the disc. Infra-red observations (sensitive to dust) would be dominated by the light from the thick inner edge of the disc. Sub-millimetre observations (sensitive to gas velocities) would appear to be hot in `turbulent' motions (actually the ordered motion caused by the passage of the spiral arms), but cold in chemistry. Resolved sub-millimetre maps of circumstellar discs might even be able to detect the spiral arms directly.Comment: Revision adds new data, and corrects physical intepretatio