Assessing cosmic acceleration with the Alcock–Paczyński effect in the SDSS-IV quasar catalogue

ABSTRACT The geometry of the Universe may be probed using the Alcock–Paczyński (AP) effect, in which the observed redshift size of a spherical distribution of sources relative to its angular size varies according to the assumed cosmological model. Past applications of this effect have been limited, however, by a paucity of suitable sources and mitigating astrophysical factors, such as internal redshift-space distortions and poorly known source evolution. In this Letter, we introduce a new test based on the AP effect that avoids the use of spatially bound systems, relying instead on sub-samples of quasars at redshifts z ≲ 1.5 in the Sloan Digital Sky Survey IV, with a possible extension to higher redshifts and improved precision when this catalogue is expanded by upcoming surveys. We here use this method to probe the redshift-dependent expansion rate in three pertinent Friedmann–Lemaître–Robertson–Walker cosmologies: Λ cold dark matter (ΛCDM), which predicts a transition from deceleration to acceleration at z ∼ 0.7; Einstein–de Sitter, in which the Universe is always decelerating; and the Rh = ct universe, which expands at a constant rate. ΛCDM is consistent with these data, but Rh = ct is favoured overall.

Synthesis, Characterization and Some Biological Properties of PVA/PVP/PN Hydrogel Nanocomposites: Antibacterial and Biocompatibility

In this study, it was aimed to synthesize hydrogel based antibacterial, biocompatible and non-toxic wound dressing materials by solvent removal method usingpoly(vinylalcohol) (PVA), poly(vinylpyrolidone) (PVP) and nano pomegranate seed (PN).The morphology, swelling capacity, contact angle, antibacterial activity, biocompatibility and cytotoxicity of the synthesized films were determined. From the experimental findings, it was found that the PN particles were nano-sized, showed homogeneous and spherical distribution and improved the hydrophobic properties of the materials obtained by the addition of PN. And also, their swelling capacities were decreased with increased PN amount and all of the materials showed similar antibacterial activity, hemocompatibility and cytotoxicity.

Spherical recurrence and locally isometric embeddings of trees into positive density subsets of ℤd

Magyar has shown that if B ⊂ ℤd has positive upper density (d ⩾ 5), then the set of squared distances {||b1 − b2||2 : b1, b2 ∈ B} contains an infinitely long arithmetic progression, whose period depends only on the upper density of B. We extend this result by showing that B contains locally isometrically embedded copies of every tree with edge lengths in some given arithmetic progression (whose period depends only on the upper density of B and the number of vertices of the sought tree). In particular, B contains all chains of elements with gaps in some given arithmetic progression (which depends on the length of the sought chain). This is a discrete analogue of a result obtained recently by Bennett, Iosevich and Taylor on chains with prescribed gaps in sets of large Haussdorf dimension. Our techniques are Ergodic theoretic and may be of independent interest to Ergodic theorists. In particular, we obtain Ergodic theoretic analogues of recent optimal spherical distribution results of Lyall and Magyar which, via Furstenberg's correspondence principle, recover their combinatorial results.