Constraints on dark energy and modified gravity models by the Cosmological Redshift Drift test

We study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time acceleration, within the framework of General Theory of Relativity (GR) (XCDM, scalar field potentials) and beyond GR (f(R)$f(R)$ gravity model).     

Surface‐enhanced resonance Raman spectroscopic characterization of cytochrome c immobilized on 2‐mercaptoethanesulfonate monolayers on silver

Single‐component self‐assembled monolayers (SAMs) of mercaptoethanesulfonate (MES) on Ag surfaces were studied with surface‐enhanced resonance Raman scattering (SERRS) spectroscopy with a view to their application to immobilize (ferro)cytochrome c (cyt c). SERS studies revealed that MES molecules adopt primarily trans (T) conformation even at early stages of the SAM growth and over wide range of pH values. High accessibility of the negatively charged groups for (bio)molecules in solution makes single‐component MES SAMs suitable linkage monolayers for electrostatic attachment of cyt c, which was verified with SERRS. Cyt c was successfully anchored to MES‐coated Ag at natural (∼5), neutral, and isoelectric point (10.6) pH. At pH = 7.0 and 10.6, SERRS bands characteristic of native six‐coordinated low‐spin (6cLS) heme iron configuration were detected. Lack of buffering resulted in additional appearance of five‐coordinated high‐spin (5cHS) SERRS markers and the presence of bands indicating ferric ion. An electrostatic attraction between protein and SAM was confirmed to exclude the hydrophobic interactions involved in cyt c binding. Cyt c attached to MES SAM on Ag was found to be electroactive at neutral pH, and protein oxidation was assisted with reversible conversion of 6cLS to the non‐native 5cHS state. Alteration of heme orientation deduced from SERRS spectra upon change of redox state allowed us to propose the protein dynamics as the electron transfer rate‐limiting step. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessment of cardiac iron by MRI susceptometry and R2* in patients with thalassemia

A magnetic resonance imaging cardiac magnetic susceptometry (MRI-CS) technique for assessing cardiac tissue iron concentration based on phase mapping was developed. Normal control subjects (n=9) and thalassemia patients (n=13) receiving long-term blood transfusion therapy underwent MRI-CS and MRI measurements of the cardiac relaxation rate R2*. Using MRI-CS, subepicardium and subendocardium iron concentrations were quantified exploiting the hemosiderin/ferritin iron specific magnetic susceptibility. The average of subepicardium and subendocardium iron concentrations and R2* of the septum were found to be strongly correlated (r=0.96, P<.0001), and linear regression analysis yielded CIC (μg Fe/g_{wet tissue})=(6.4±0.4)·R2* _septum (s⁻¹) − (120±40). The results demonstrated that septal R2* indeed measures cardiac iron level.     

A New Semi-conductive Copper(I) Halide Coordination Polymer: Synthesis, Structure, and Theoretical Study

Abstract  A 1-D hybrid copper(I) halides, [(phen)Cu₃I₃] _n (phen = 1,10-phenanthroline)(1) with novel D6R (double six-membered rings) Cu₆I₆ cores, was synthesized by solvothermal reaction and characterized by single-crystal X-ray diffraction. In 1, nitrogen atoms from phen replace two I of CuI₄ tetrahedron to give distorted tetrahedral geometries (CuI₂N₂), then CuI₂N₂ tetrahedron shares corners via μ₃-I to generate an extended 1-D zigzag chain. Two zigzag chains combines with one 1-D (Cu₄I₄) _n chain containing D6R cores via μ₃-I-Cu (from cores) bonds to form the infinite 1-D ribbonlike polymer along the a-axis. Furthermore, the title compound is stabilized by conspicuous C–H···I hydrogen bonds, π–π and d¹⁰–d¹⁰ metallic interactions. Experimental and theoretical optical property investigation indicates that 1 possesses semiconductor property. DFT calculation was executed to probe the electronic structure of 1. To our interest, phen act as a property control species with its π* electrons appear in the forbidden band. Graphical Abstract  A hybrid copper(I) halides [(phen)Cu₃I₃] _n containing D6R cores was structurally determined, which was stabilized by conspicuous C–H···I hydrogen bonds, π–π and d¹⁰–d¹⁰ metallic interactions and possesses semiconductor property. DFT calculation indicate phen act as a property control species with its π* electrons appear in the forbidden band. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Inverse scattering problem for nonstationary Dirac-type systems on the half-plane

In this paper was considered the scattering problem for the nonstationary Dirac-type systems of n (n?2) equations on the half-plane when the system has n₁ (1?n₁?n−1) incident and n₂ (n₂=n−n₁) scattered waves. In case n₁ is divisible by n₂, we formulate the inverse scattering problem for a nonstationary Dirac-type system when considering m () scattering problems on the half-plane with the same incident waves but different boundary conditions. Moreover, the scattering operator for the nonstationary Dirac-type system on half-plane was defined and unique restoration of the potential with respect to the scattering operator was proved.     

Enlargement of the group of circular units of a bicyclic field

We compute the index of a certain extension of Sinnott's group of circular units in the group of all units of a bicyclic field. From this index we obtain some divisibility properties for class numbers of bicyclic fields.     

Image of the group ring of the Galois representation associated to Drinfeld modules

Let φ be a Drinfeld A-module of arbitrary rank and arbitrary characteristic over a finitely generated field K, and set GK=Gal(Ksep/K). Let E=EndK(φ). We show that for almost all primes p of A the image of the group ring A[GK] in EndA(Tp(φ)) is the commutant of E. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p](Ksep) of φ is absolutely irreducible for almost all p.     

Powers of roots in linear spaces

Suppose K is a field, αn∈K^∗, and n is the least natural number with this property. We study the question on how many powers αj, 0?j<n, lie in a given K-linear space.     

A parabolic two-phase obstacle-like equation

For the parabolic obstacle-problem-like equation

Δu−t_∂u=λ₊χ{u>0}−λ₋χ{u<0},