Log-convexity and log-concavity of hypergeometric-like functions

We find sufficient conditions for log-convexity and log-concavity for the functions of the forms $a\mapsto\sum{f_k}(a)_kx^k$, $a\mapsto\sum{f_k}\Gamma(a+k)x^k$ and $a\mapsto\sum{f_k}x^k/(a)_k$. The most useful examples of such functions are generalized hypergeometric functions. In particular, we generalize the Tur\'{a}n inequality for the confluent hypergeometric function recently proved by Barnard, Gordy and Richards and log-convexity results for the same function recently proved by Baricz. Besides, we establish a reverse inequality which complements naturally the inequality of Barnard, Gordy and Richards. Similar results are established for the Gauss and the generalized hypergeometric functions. A conjecture about monotonicity of a quotient of products of confluent hypergeometric functions is made.Comment: 13 pages, no figure

Delay Equations and Radiation Damping

Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we identify this invariant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not contained in the local equations of motion.Comment: 15 pages, 1 figure, a paragraph added on page 5; 3 references adde

The 13-C(p,d) Reaction at 120 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Frequent copy number gains of SLC2A3 and ETV1 in testicular embryonal carcinomas

Testicular germ cell tumours (TGCTs) appear as different histological subtypes or mixtures of these. They show similar, multiple DNA copy number changes, where gain of 12p is pathognomonic. However, few high-resolution analyses have been performed and focal DNA copy number changes with corresponding candidate target genes remain poorly described for individual subtypes. We present the first high-resolution DNA copy number aberration (CNA) analysis on the subtype embryonal carcinomas (ECs), including 13 primary ECs and 5 EC cell lines. We identified recurrent gains and losses and allele-specific CNAs. Within these regions, we nominate 30 genes that may be of interest to the EC subtype. By in silico analysis of data from 150 TGCTs from The Cancer Genome Atlas (TCGA), we further investigated CNAs, RNA expression, somatic mutations and fusion transcripts of these genes. Among primary ECs, ploidy ranged between 2.3 and 5.0, and the most common aberrations were DNA copy number gains at chromosome (arm) 7, 8, 12p, and 17, losses at 4, 10, 11, and 18, replicating known TGCT genome characteristics. Gain of whole or parts of 12p was found in all samples, including a highly amplified 100 kbp segment at 12p13.31, containing SLC2A3. Gain at 7p21, encompassing ETV1, was the second most frequent aberration. In conclusion, we present novel CNAs and the genes located within these regions, where the copy number gain of SLC2A3 and ETV1 are of interest, and which copy number levels also correlate with expression in TGCTs

Barrier effects on the collective excitations of split Bose-Einstein condensates

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure

UK Environmental Change Network stakeholder consultation

During the Environmental Change Network (ECN) site mangers meeting feedback on the role of UK-SCAPE funding was sought. Representatives from collaborating institutions did not restrict their comments to only the period of UK-SCAPE, as this program is a continuation of previous national capability funding. The stakeholders present appreciated the role of UKCEH through the processes of co-design, co-delivery and co-development in shaping the ECN. They further commented on the co-dependency conferred by the network for their institutions and sites. While several stakeholders noted that they could not benefit directly from UK-SCAPE funding they recognised that funding was required for coordination of the network in addition to collecting monitoring data. They highlighted the risk of failure of the network and the lost opportunities in terms of collaborative working and data delivery to the research community if funding is not maintained in the network

Energy band structure and intrinsic coherent properties in two weakly linked Bose Einstein Condensates

The energy band structure and energy splitting due to quantum tunneling in two weakly linked Bose-Einstein condensates were calculated by using the instanton method. The intrinsic coherent properties of Bose Josephson junction were investigated in terms of energy splitting. For $E_{C}/E_{J}\ll 1$, the energy splitting is small and the system is globally phase coherent. In the opposite limit, $E_{C}/E_{J}\gg 1$, the energy splitting is large and the system becomes a phase dissipation. Our reslults suggest that one should investigate the coherence phenomna of BJJ in proper condition such as $E_{C}/E_{J}\sim 1$.Comment: to appear in Phys. Rev. A, 2 figure

Disparate MgII Absorption Statistics towards Quasars and Gamma-Ray Bursts : A Possible Explanation

We examine the recent report by Prochter et al. (2006) that gamma-ray burst (GRB) sight lines have a much higher incidence of strong MgII absorption than quasar sight lines. We propose that the discrepancy is due to the different beam sizes of GRBs and quasars, and that the intervening MgII systems are clumpy with the dense part of each cloudlet of a similar size as the quasars, i.e. < 10^16 cm, but bigger than GRBs. We also discuss observational predictions of our proposed model. Most notably, in some cases the intervening MgII absorbers in GRB spectra should be seen varying, and quasars with smaller sizes should show an increased rate of strong MgII absorbers. In fact, our prediction of variable MgII lines in the GRB spectra has been now confirmed by Hao et al. (2007), who observed intervening FeII and MgII lines at z=1.48 to be strongly variable in the multi-epoch spectra of z=4.05 GRB060206.Comment: 12 pages, 2 figures; substantially revised model calculation; accepted for publication in Astrophysics & Space Science as a Lette

Magnetic fields in protoplanetary disks

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary discs. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface, and magnetically-driven mixing has implications for disk chemistry and evolution of the grain population. However, the weak ionisation of protoplanetary discs means that magnetic fields may not be able to effectively couple to the matter. I present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas. For a standard population of 0.1 micron grains the active surface layers have a combined column of about 2 g/cm^2 at 1 AU; by the time grains have aggregated to 3 microns the active surface density is 80 g/cm^2. In the absence of grains, x-rays maintain magnetic coupling to 10% of the disk material at 1 AU (150 g/cm^2). At 5 AU the entire disk thickness becomes active once grains have aggregated to 1 micron in size.Comment: 11 pages, 11 figs, aastex.cls. Accepted for publication in Astrophysics & Space Science. v3 corrects bibliograph

A Circumplanetary Disk around PDS70c

International audiencePDS 70 is a unique system in which two protoplanets, PDS 70 b and c, have been discovered within the dust-depleted cavity of their disk, at ~22 and 34 au, respectively, by direct imaging at infrared wavelengths. Subsequent detection of the planets in the Hα line indicates that they are still accreting material through circumplanetary disks. In this Letter, we present new Atacama Large Millimeter/submillimeter Array (ALMA) observations of the dust continuum emission at 855 μm at high angular resolution (~20 mas, 2.3 au) that aim to resolve the circumplanetary disks and constrain their dust masses. Our observations confirm the presence of a compact source of emission co-located with PDS 70 c, spatially separated from the circumstellar disk and less extended than ~1.2 au in radius, a value close to the expected truncation radius of the circumplanetary disk at a third of the Hill radius. The emission around PDS 70 c has a peak intensity of ~86 ± 16 μJy beam-1, which corresponds to a dust mass of ~0.031 M⊕ or ~0.007 M⊕, assuming that it is only constituted of 1 μm or 1 mm sized grains, respectively. We also detect extended, low surface brightness continuum emission within the cavity near PDS 70 b. We observe an optically thin inner disk within 18 au of the star with an emission that could result from small micron-sized grains transported from the outer disk through the orbits of b and c. In addition, we find that the outer disk resolves into a narrow and bright ring with a faint inner shoulder