Spectral expansion for singular conformable fractional Sturm-Liouville problem

With this study, the spectral function for singular conformable fractional Sturm-Lioville problem is demonstrated. Further, we establish a Parseval equality and spectral expansion formula by terms of the spectral function

Spectral expansion for singular conformable fractional Sturm-Liouville problem

With this study, the spectral function for singular conformable fractional Sturm-Lioville problem is demonstrated. Further, we establish a Parseval equality and spectral expansion formula by terms of the spectral function

An Unexpectedly Swift Rise in the Gamma-ray Burst Rate

The association of long gamma-ray bursts with supernovae naturally suggests that the cosmic GRB rate should trace the star formation history. Finding otherwise would provide important clues concerning these rare, curious phenomena. Using a new estimate of Swift GRB energetics to construct a sample of 36 luminous GRBs with redshifts in the range z=0-4, we find evidence of enhanced evolution in the GRB rate, with ~4 times as many GRBs observed at z~4 than expected from star formation measurements. This direct and empirical demonstration of needed additional evolution is a new result. It is consistent with theoretical expectations from metallicity effects, but other causes remain possible, and we consider them systematically.Comment: 4 pages, 4 figures; minor changes to agree with published versio

Stringent Constraint on Galactic Positron Production

The intense 0.511 MeV gamma-ray line emission from the Galactic Center observed by INTEGRAL requires a large annihilation rate of nonrelativistic positrons. If these positrons are injected at even mildly relativistic energies, higher-energy gamma rays will also be produced. We calculate the gamma-ray spectrum due to inflight annihilation and compare to the observed diffuse Galactic gamma-ray data. Even in a simplified but conservative treatment, we find that the positron injection energies must be $\lesssim 3$ MeV, which strongly constrains models for Galactic positron production.Comment: 4 pages, 2 figures; minor revisions, accepted for publication in PR

Dynamic phase transition properties and hysteretic behavior of a ferrimagnetic core-shell nanoparticle in the presence of a time dependent magnetic field

We have presented dynamic phase transition features and stationary-state behavior of a ferrimagnetic small nanoparticle system with a core-shell structure. By means of detailed Monte Carlo simulations, a complete picture of the phase diagrams and magnetization profiles have been presented and the conditions for the occurrence of a compensation point $T_{comp}$ in the system have been investigated. According to N\'{e}el nomenclature, the magnetization curves of the particle have been found to obey P-type, N-type and Q-type classification schemes under certain conditions. Much effort has been devoted to investigation of hysteretic response of the particle and we observed the existence of triple hysteresis loop behavior which originates from the existence of a weak ferromagnetic core coupling $J_{c}/J_{sh}$, as well as a strong antiferromagnetic interface exchange interaction $J_{int}/J_{sh}$. Most of the calculations have been performed for a particle in the presence of oscillating fields of very high frequencies and high amplitudes in comparison with exchange interactions which resembles a magnetic system under the influence of ultrafast switching fields. Particular attention has also been paid on the influence of the particle size on the thermal and magnetic properties, as well as magnetic features such as coercivity, remanence and compensation temperature of the particle. We have found that in the presence of ultrafast switching fields, the particle may exhibit a dynamic phase transition from paramagnetic to a dynamically ordered phase with increasing ferromagnetic shell thickness.Comment: 12 pages, 12 figure

On the dissipative conformable fractional singular Sturm-Liouville operator

In this study, a dissipative conformable fractional singular Sturm–Liouville operator is studied. For this operator, a completeness theorem is proved by Krein’s theorem

The Centaurus A Ultrahigh-Energy Cosmic Ray Excess and the Local Extragalactic Magnetic Field

The ultrahigh-energy cosmic-ray anisotropies discovered by the Pierre Auger Observatory give the potential to finally address both the particles' origins and properties of the nearby extragalactic magnetic field (EGMF). We examine the implications of the excess of ~ 10^20 eV events around the nearby radio galaxy Centaurus A. We find that, if Cen A is the source of these cosmic rays, the angular distribution of events constrains the EGMF strength within several Mpc of the Milky Way to > 20 nG for an assumed primary proton composition. Our conclusions suggest that either the observed excess is a statistical anomaly or the local EGMF is stronger then conventionally thought. We discuss the implications of this field, including UHECR scattering from more distant sources, time delays from transient sources, and the possibility of using magnetic lensing signatures to attain tighter constraints.Comment: 8 pages, 8 figures; Matches published version in AP

A somatic origin of homologous Robertsonian translocations and isochromosomes

One t(14q14q), three t(15q15q), two t(21q21q), and two t(22q22q) nonmosaic, apparently balanced, de novo Robertsonian translocation cases were investigated with polymorphic markers to establish the origin of the translocated chromosomes. Four cases had results indicative of an isochromosome: one t(14q14q) case with mild mental retardation and maternal uniparental disomy (UPD) for chromosome 14, one t(15q15q) case with the Prader-Willi syndrome and UPD(15), a phenotypically normal carrier of t(22q22q) with maternal UPD(22), and a phenotypically normal t(21q21q) case of paternal UPD(21). All UPD cases showed complete homozygosity throughout the involved chromosome, which is supportive of a postmeiotic origin. In the remaining four cases, maternal and paternal inheritance of the involved chromosome was found, which unambiguously implies a somatic origin. One t(15q15q) female had a child with a ring chromosome 15, which was also of probable postmeiotic origin as recombination between grandparental haplotypes had occurred prior to ring formation. UPD might be expected to result from de novo Robertsonian translocations of meiotic origin; however, all de novo homologous translocation cases, so far reported, with UPD of chromosomes 14, 15, 21, or 22 have been isochromosomes. These data provide the first direct evidence that nonmosaic Robertsonian translocations, as well as isochromosomes, are commonly the result of a mitotic exchange

Evidence for Low Extinction in Actively Star Forming Galaxies at z>>6.5

We present a search for the [CII] 158micron fine structure line (a main cooling line of the interstellar medium) and the underlying far-infrared (FIR) continuum in three high-redshift (6.6<z<8.2) star-forming galaxies using the IRAM Plateau de Bure interferometer. We targeted two Lyman-Alpha-selected galaxies (Lyman-Alpha-Emitters, LAEs) with moderate UV-based star formation rates (SFR~20 M_sun/yr; Himiko at z=6.6 and IOK-1 at z=7.0) and a Gamma Ray Burst (GRB) host galaxy (GRB 090423 at z~8.2). Based on our 3 sigma rest-frame FIR continuum limits, previous (rest-frame) UV continuum measurements and spectral energy distribution (SED) fitting, we rule out SED shapes similar to highly obscured galaxies (e.g. Arp220, M82) and less extreme dust-rich nearby spiral galaxies (e.g. M51) for the LAEs. Conservatively assuming a SED shape typical of local spiral galaxies we derive upper limits for the FIR-based star formation rates (SFRs) of ~70 M_sun/yr, ~50 M_sun/yr and ~40 M_sun/yr for Himiko, IOK-1 and GRB 090423, respectively. For the LAEs these limits are only a factor ~3 higher than the published UV-based SFRs (uncorrected for extinction). This indicates that the dust obscuration in the z>6 LAEs studied here is lower by a factor of a few than what has recently been found in some LAEs at lower redshift (2<z<3.5) with similar UV-based SFRs. A low obscuration in our z>6 LAE sample is consistent with recent rest-frame UV studies of z~7 Lyman-Break-Galaxies (LBGs).Comment: Accepted for publication in the Astrophysical Journa