The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

We construct a braided version of Thompson's group V.Comment: 27 page

Connectedness properties of the set where the iterates of an entire function are unbounded

We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded

An explanation of the Newman-Janis Algorithm

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

We show that the minimal speed for the existence of monotonic fronts of the equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in $(0,1)$ derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$ when $f'(0)=0$ is included as an extension of the results.Comment: Latex, postcript figure availabl

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Boulder trains in western Massachusetts

Guidebook for field trips in western Massachusetts, northern Connecticut and adjacent areas of New York: 67th annual meeting October 10, 11, and 12, 1975: Trip C-

The Universal Cut Function and Type II Metrics

In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years - from the work of Hermann Bondi - that energy and momentum of gravitational sources could be determined by similar integrals of the asymptotic Weyl tensor. Recently we observed that there were certain overlooked structures, {defined at future null infinity,} that allowed one to determine (or define) further properties of both electromagnetic and gravitating sources. These structures, families of {complex} `slices' or `cuts' of Penrose's null infinity, are referred to as Universal Cut Functions, (UCF). In particular, one can define from these structures a (complex) center of mass (and center of charge) and its equations of motion - with rather surprising consequences. It appears as if these asymptotic structures contain in their imaginary part, a well defined total spin-angular momentum of the source. We apply these ideas to the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page

Oxylipins in triglyceride-rich lipoproteins of dyslipidemic subjects promote endothelial inflammation following a high fat meal.

Elevated triglyceride-rich lipoproteins (TGRL) in circulation is a risk factor for atherosclerosis. TGRL from subjects consuming a high saturated fat test meal elicited a variable inflammatory response in TNFα-stimulated endothelial cells (EC) that correlated strongly with the polyunsaturated fatty acid (PUFA) content. This study investigates how the relative abundance of oxygenated metabolites of PUFA, oxylipins, is altered in TGRL postprandially, and how these changes promote endothelial inflammation. Human aortic EC were stimulated with TNFα and treated with TGRL, isolated from subjects' plasma at fasting and 3.5 hrs postprandial to a test meal high in saturated fat. Endothelial VCAM-1 surface expression stimulated by TNFα provided a readout for atherogenic inflammation. Concentrations of esterified and non-esterified fatty acids and oxylipins in TGRL were quantified by mass spectrometry. Dyslipidemic subjects produced TGRL that increased endothelial VCAM-1 expression by ≥35%, and exhibited impaired fasting lipogenesis activity and a shift in soluble epoxide hydrolase and lipoxygenase activity. Pro-atherogenic TGRL were enriched in eicosapentaenoic acid metabolites and depleted in esterified C18-PUFA-derived diols. Abundance of these metabolites was strongly predictive of VCAM-1 expression. We conclude the altered metabolism in dyslipidemic subjects produces TGRL with a unique oxylipin signature that promotes a pro-atherogenic endothelial phenotype

A new chelonibiid from the Miocene of Zanzibar (Eastern Africa) sheds light on the evolution of shell architecture in turtle and whale barnacles (Cirripedia: Coronuloidea)

The fossil history of turtle and whale barnacles (Coronuloidea: Chelonibiidae, Platylepadidae, Coronulidae and †Emersoniidae) is fragmentary and has only been investigated in part. Morphological inferences and molecular phylogenetic analyses on extant specimens suggest that the roots of whale barnacles (Coronulidae) are to be found among the chelonibiid turtle barnacles, but the hard-part modifications that enabled early coronuloids to attach to the cetacean skin are still largely to be perceived. Here, we reappraise a fossil chelonibiid specimen from the Miocene of insular Tanzania that was previously referred to the living species Chelonibia caretta. This largely forgotten specimen is here described as the holotype of the new species †Chelonibia zanzibarensis. While similar to C. caretta, †C. zanzibarensis exhibits obvious external longitudinal parietal canals occurring in-between external longitudinal parietal septa that abut outwards to form T-shaped flanges, a character so far regarded as proper of the seemingly more derived Coronulidae and Platylepadidae. Along with these features, the presence of a substrate imprint on the shell exterior indicates that †C. zanzibarensis grasped its host's integument in much the same way as coronulids and platylepadids, albeit without the development of macroscopic parietal buttresses and bolsters. Thin section analyses of the inner parietal architecture of some extant and extinct coronuloids conclusively demonstrate that vestiges of comparable external parietal microstructures are present in some living members of Chelonibiidae. This observation strengthens the unity of Coronuloidea while significantly contributing to our understanding of the evolution of the coronuloid shell structure in adapting to a diverse spectrum of hosts