Integer solutions of a sequence of decomposable form inequalities

In this paper, we prove the finiteness of the number of integer solutions of the decomposable form inequalities. We also study the number of integer solutions of a sequence of decomposable form inequalities

Reflexivity of the automorphism and isometry groups of the suspension of B(H)B(H)

The aim of this paper is to show that the automorphism and isometry groups of the suspension of $B(H)$, $H$ being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of $C_0(\mathbb R)\otimes B(H)$ is an automorphism, respectively a surjective isometry

Can the MDCDW condensate withstand the heat of a cold neutron star?

The correct description of strongly interacting matter at low temperatures and moderately high densities—in particular the conditions realized inside neutron stars—is still unknown. We review some recent results on the magnetic dual chiral density wave (MDCDW) phase, a candidate phase of quark matter for this region of the QCD phase diagram. We highlight the effects of magnetic fields and temperature on the condensate, which can be explored using a high-order Ginzburg-Landau (GL) expansion. We also explain how the condensate\u27s nontrivial topology, which arises due to the asymmetry in the lowest Landau level modes, affects its physical properties. Finally, we comment on the possible relevance of these results to neutron star applications. Over a wide range of densities and magnetic field strengths, MDCDW is preferred over the chirally symmetric ground state at temperatures consistent with typical cold neutron stars, and in some cases, even hot ones

Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.Comment: 16 page

Larval ecology and synchronous reproduction of two crustacean species : Semibalanus balanoides in New England, USA and Gecarcinus quadratus in Veraguas, Panama

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2011The environmental cues for synchronous reproduction were investigated for two highly abundant, ecologically important crustacean species: the temperate acorn barnacle, Semibalanus balanoides, and the tropical terrestrial crab, Gecarcinus quadratus. Larval ecology of these two species was also studied to determine potential sources of larval mortality and recruitment success. High-frequency observations revealed that early-stage larval abundance of S. balanoides was related to storms, and possibly turbidity. Field observations and experiments studied the effect of turbidity and phytoplankton on larval release response. Release coincided with increased turbidity at three sites along the northeast coast of the United States. A three-year time series of phytoplankton and zooplankton data showed that larval release was not consistently related to phytoplankton abundance (total or single species). When gravid barnacles were exposed to phytoplankton or synthetic beads, they released in response to both, suggesting that presence of particles is more important than identity of particles. Feeding experiments showed that adult cannibalism on newly released larvae is lower in highly turbid conditions. It is suggested here that S. balanoides synchronizes its reproduction with the onset of phytoplankton blooms, but turbidity may fine-tune the timing if it provides predation refuge for larvae. Adult G. quadratus females undertake synchronized breeding migrations to the ocean after the first rains of the rainy season, presumably when the risk of desiccation is lowest. They wait for darkness and an ebbing tide before releasing their eggs into the water. First-stage zoeas have dark pigmentation, long dorsal and rostral spines, and a pair of lateral spines. Hatching in darkness may help zoeas avoid predation from planktivorous diurnal fish, and the zoeal spines may deter predation from planktivorous nocturnal fish. In the laboratory, a G. quadratus zoea reached the megalopa stage in 21 days. A mass migration of megalopae and juveniles out of the water was observed 30 days after adult females released their eggs. Plankton pump samples taken near the island suggest that zoea abundance and distribution may be related to the phase of the internal tide. Synchronous reproduction in these two species appears to be the result of predator avoidance behaviors.My funding was provided by a National Science Foundation Graduate Research Fellowship, three WHOI Ocean Life Institute grants (Grant # 27071337, 27071342, and 25051361), two WHOI Coastal Ocean Institute grants (Grant # 32031022 and 27040136), and financial support from the WHOI Academic Programs Office

Phase transitions and resilience of the magnetic dual chiral density wave phase at finite temperature and density

We study the phase transitions at finite temperature and density of the magnetic dual chiral density wave (MDCDW) phase. This spatially inhomogeneous phase emerges in cold, dense QCD in the presence of a strong magnetic field. Starting from the generalized Ginzburg-Landau (GL) expansion of the free energy, we derive several analytical formulas that enable fast numerical computation of the expansion coefficients to arbitrary order, allowing high levels of precision in the determination of the physical dynamical parameters, as well as in the transition curves in the temperature vs chemical potential plane at different magnetic fields. At magnetic fields and temperatures compatible with neutron star (NS) conditions, the MDCDW remains favored over the symmetric ground state at all densities. The phase’s “resilience” manifests in (1) a region of small but nonzero remnant mass and significant modulation at intermediate densities, originating in part from the nontrivial topology of the lowest Landau level, and (2) a region of increasing condensate parameters at high densities. Our analysis suggests the MDCDW condensate remains energetically favored at densities and temperatures much higher than previously considered, opening the possibility for this phase to be a viable candidate for the matter structure of even young neutron stars produced by binary neutron star (BNS) mergers

Turbidity triggers larval release by the intertidal barnacle Semibalanus balanoides

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Inter-Research for personal use, not for redistribution. The definitive version was published in Marien Ecology Progress Series 476 (2013): 141-151, doi:10.3354/meps10186.Gravid adults of the common intertidal barnacle Semibalanus balanoides (L.) brood fully developed larvae until individuals perceive some cue from the environment that triggers synchronous larval release. The prevailing hypothesis has been that phytoplankton blooms trigger release because they provide a food source for nauplius larvae. Through observations and field experiments, we tested the hypothesis that turbidity from any source, not just phytoplankton blooms, can trigger release. We documented five larval release events at three sites in the northeastern United States. Two events coincided with chlorophyll increases, and all five coincided with turbidity increases. In experiments, the larval release response was equivalent when adults were exposed to diatoms or inert synthetic beads, and it was significantly higher than under exposure to filtered seawater. We also tested the hypothesis that turbidity can decrease the risk of cannibalism for newly-released nauplii. Under experimentally manipulated conditions, adults consumed significantly fewer nauplii in a high-turbidity environment. We suggest that reproduction in this species may have evolved to coincide roughly with the local onset of winter/spring phytoplankton blooms, but the timing of larval release may have been fine-tuned further by cannibalism and predation pressures. The potential for turbid conditions to serve as a refuge for planktonic larvae of other marine organisms merits further investigation.Support for this work came from a National Science Foundation Graduate Research Fellowship and a student award from the Coastal Ocean Institute at Woods Hole Oceanographic Institution (both to JG)