Existence of certain compact contractible manifolds containing disjoint spines

A polyhedron K in the interior of a compact PL manifold M (with boundary) is said to be a (PL) spine of M provided M collapses to K. The manifold M has disjoint spines provided it collapses (independently) to two disjoint such polyhedra in its interior. A long-standing conjecture asserts that a certain class of compact, contractible 4-manifolds constructed by Mazur do not have disjoint spines. More recently, the question as to which compact, contractible manifolds have a pair of disjoint spines has been expanded by C. Guilbault so as to include other compact, contractible manifolds, including those in higher dimensions. A technique of M.H.A. Newman provides compact, contractible manifolds which are not balls. A Newman manifold is constructed as the closure of the complement of a regular neighborhood of a non-simply connected, finite, acyclic, simplicial complex. K, in Sn for sufficiently large n. When well-defined, it is denoted New(K, n). Guilbault has shown that if K is a non-simply connected, finite, acyclic, simplicial k-complex, then, New(K, n) has disjoint spines provided n \u3e 4k. His techniques, thereby, provide interesting examples of disjoint spine phenomena in dimensions n ≥ 9 and are the only known examples of such occurrences. In this work, it is shown that the result holds in dimension n = 4k as well. Moreover, if K is a non-simply connected, finite, acyclic 2-complex, it is shown that New(K, n) has disjoint spines if n ≥ 5, thereby producing relatively low-dimensional examples of the phenomenon. Since it is known that no interesting examples can occur in dimensions n ≤ 3, these results show that the question regarding existence of interesting examples is, now, undecided only in dimension 4

Gravitational polarization and the phenomenology of MOND

The modified Newtonian dynamics (MOND) has been proposed as an alternative to the dark matter paradigm; the philosophy behind is that there is no dark matter and we witness a violation of the Newtonian law of dynamics. In this article, we interpret differently the phenomenology sustaining MOND, as resulting from an effect of "gravitational polarization", of some cosmic fluid made of dipole moments, aligned in the gravitational field, and representing a new form of dark matter. We invoke an internal force, of non-gravitational origin, in order to hold together the microscopic constituents of the dipole. The dipolar particles are weakly influenced by the distribution of ordinary matter; they are accelerated not by the gravitational field, but by its gradient, or tidal gravitational field.Comment: 14 pages, 1 figure, to appear in Classical and Quantum Gravit

Generalized virial theorem in Palatini f(R)f(R) gravity

We use the collision-free Boltzmann equation in Palatini $f({\mathcal{R}})$ gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contribute to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in cluster of galaxies. We then derive the velocity dispersion relation for clusters followed by the metric tensor components inside the cluster as well as the $f({\mathcal{R}})$ lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the $f({\mathcal{R}})$ virial theorem is a convenient tool to test the viability of $f({\mathcal{R}})$ theories in different models. Finally, we discuss the limitations of our approach in the light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work.Comment: 16 pages, to appear in PR

The COOH terminus of the c-Abl tyrosine kinase contains distinct F- and G-actin binding domains with bundling activity

The myristoylated form of c-Abl protein, as well as the P210bcr/abl protein, have been shown by indirect immunofluorescence to associate with F-actin stress fibers in fibroblasts. Analysis of deletion mutants of c-Abl stably expressed in fibroblasts maps the domain responsible for this interaction to the extreme COOH-terminus of Abl. This domain mediates the association of a heterologous protein with F-actin filaments after microinjection into NIH 3T3 cells, and directly binds to F-actin in a cosedimentation assay. Microinjection and cosedimentation assays localize the actin-binding domain to a 58 amino acid region, including a charged motif at the extreme COOH-terminus that is important for efficient binding. F-actin binding by Abl is calcium independent, and Abl competes with gelsolin for binding to F- actin. In addition to the F-actin binding domain, the COOH-terminus of Abl contains a proline-rich region that mediates binding and sequestration of G-actin, and the Abl F- and G-actin binding domains cooperate to bundle F-actin filaments in vitro. The COOH terminus of Abl thus confers several novel localizing functions upon the protein, including actin binding, nuclear localization, and DNA binding. Abl may modify and receive signals from the F-actin cytoskeleton in vivo, and is an ideal candidate to mediate signal transduction from the cell surface and cytoskeleton to the nucleus

The virial theorem and the dynamics of clusters of galaxies in the brane world models

A version of the virial theorem, which takes into account the effects of the non-compact extra-dimensions, is derived in the framework of the brane world models. In the braneworld scenario, the four dimensional effective Einstein equation has some extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. To derive the generalized virial theorem we use a method based on the collisionless Boltzmann equation. The dark radiation term generates an equivalent mass term (the dark mass), which gives an effective contribution to the gravitational energy. This term may account for the well-known virial theorem mass discrepancy in actual clusters of galaxies. An approximate solution of the vacuum field equations on the brane, corresponding to weak gravitational fields, is also obtained, and the expressions for the dark radiation and dark mass are derived. The qualitative behavior of the dark mass is similar to that of the observed virial mass in clusters of galaxies. We compare our model with the observational data for galaxy clusters, and we express all the physical parameters of the model in terms of observable quantities. In particular, we predict that the dark mass must extend far beyond the presently considered virial radius. The behavior of the galaxy cluster velocity dispersion in brane world models is also considered. Therefore the study of the matter distribution and velocity dispersion at the extragalactic scales could provide an efficient method for testing the multi-dimensional physical models.Comment: 29 pages, no figures, accepted for publication in PR

Brane-f(R)f(R) gravity and dark matter

The collision-free Boltzmann equation is used in the context of brane-$f(R)$ gravity to derive the virial theorem. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations and contributes to gravitational energy and that such a geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. In addition, the galaxy rotation curves are studied by utilizing the concept of conformal symmetry and notion of conformal Killing symmetry. The field equations may then be obtained in an exact parametric form in terms of the parameter representing the conformal factor. This provides the possibility of studying the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity can be derived as a function of the conformal factor and integration constants, resulting in a constant value at large radial distances. Relevant phenomenon such as the deflection of light passing through a region where the rotation curves are flat and the radar echo delay are also studied.Comment: 12 pages, 2 figures, to appear in PR

HI observations of luminous infrared galaxy mergers

A total of 19 luminous infrared galaxy mergers, with L_IR~2 10^11 L_sun for H_0=75 km/s/Mpc, have been observed in the HI line at Nancay and four of them were observed at Arecibo as well. Of these 19, ten had not been observed before. Six were clearly detected, one of which for the first time. The objective was to statistically sample the \HI gas mass in luminous infrared mergers along a starburst merger sequence where the molecular CO gas content is already known.Comment: 11 pages, accepted for Astron. Astrophys., 22/12/200

Innovative behaviour: how much transformational leadership do you need?

Studies on the effects of transformational leadership on employee innovative behaviour have yielded mixed results. The authors argue that one possible explanation for these mixed findings is that researchers have assumed a linear relationship between these constructs. In contrast, they suggest that the relationship between transformational leadership and innovative behaviour is non-linear. Specifically, the authors argue that the positive effects of transformational leadership on innovative behaviour will be stronger at low and high levels of transformational leadership. Moreover, they examine whether the relationship between transformational leadership and innovative behaviour is mediated by knowledge sharing within and between teams. The authors undertake a constructive replication by testing these hypothesized relationships in two studies: (1) a multi-actor team-level study conducted in the USA, and (2) a longitudinal employee-level study of teachers in the Netherlands. Results of both studies reveal that knowledge sharing mediates the relationship between transformational leadership and innovative behaviour, and that the indirect relationship is curvilinear. The authors link these findings to leader substitution theory, proposing that employees turn to their peers and other parties when there is an absence of effective leadership

The combined effects of treated sewage discharge and land use on rivers

Freshwater ecosystems are increasingly threatened by multiple anthropogenic stressors. Release of treated sewage effluent and pollution from agricultural or urban sources can independently reduce water quality with implications for ecological communities. However, our knowledge of the combined effects of these stressors is limited. We performed a field study to quantify the combined effect of treated sewage discharge and land use on nutrient concentrations, sewage fungus presence and communities of macroinvertebrates and benthic algae. Over three seasons in four rivers we found that a model which included an interaction between sewage pollution and time of the year (i.e. months) was the best predictor of nutrient concentrations and the abundance of algae and sewage fungus. Both macroinvertebrate and algae communities shifted downstream of sewage input. Specifically, more tolerant groups, such as cyanobacteria and oligochaetes, were more abundant. The EPT (Ephemeroptera, Plecoptera and Tricoptera) water quality score was best explained by an interaction between month and agriculture in the surrounding landscape. Overall, our results show that sewage discharge has a significant impact on water quality and benthic riverine communities, regardless of the surrounding land uses. Agricultural inputs, however, could be more important than treated sewage discharge in reducing the abundance of sensitive invertebrate taxa. We need both improvements to wastewater treatment processes and reductions in agricultural pollution to reduce threats to vulnerable freshwater communities