An Independence Result on Cotorsion Theories over Valuation Domains

AbstractIt is shown that, over suitable valuation domains R with field of quotients Q, the cotorsion theory GK generated by K=Q/R coincides with the cotorsion theory C∂ cogenerated by the Fuchs' divisible module ∂, provided that Gödel's Axiom of Constructibility V=L is assumed. On the other hand, assuming Martin's Axiom and the negation of the Continuum Hypothesis, it is proved that the cotorsion theory GK is strictly smaller than C∂ by exhibiting a strongly (ℵ1−K)-free divisible module M of projective dimension 2 such that Ext1R(M,K)=0. Applications to Whitehead modules are derived

Algebraic entropy in locally linearly compact vector spaces

We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69\u201387, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem

Disordered Fulde-Ferrel-Larkin-Ovchinnikov State in d-wave Superconductors

We study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in the disordered systems. We analyze the microscopic model, in which the d-wave superconductivity is stabilized near the antiferromagnetic quantum critical point, and investigate two kinds of disorder, namely, box disorder and point disorder, on the basis of the Bogoliubov-deGennes (BdG) equation. The spatial structure of modulated superconducting order parameter and the magnetic properties in the disordered FFLO state are investigated. We point out the possibility of "FFLO glass" state in the presence of strong point disorders, which arises from the configurational degree of freedom of FFLO nodal plane. The distribution function of local spin susceptibility is calculated and its relation to the FFLO nodal plane is clarified. We discuss the NMR measurements for CeCoIn_5.Comment: Submitted to New. J. Phys. a focus issue on "Superconductors with Exotic Symmetries

High pressure phase diagrams of CeRhIn5_5 and CeCoIn5_5 studied by ac calorimetry

The pressure-temperature phase diagrams of the heavy fermion antiferromagnet CeRhIn$_5$ and the heavy fermion superconductor CeCoIn$_5$ have been studied under hydrostatic pressure by ac calorimetry and ac susceptibility measurements using diamond anvil cells with argon as pressure medium. In CeRhIn$_5$, the use of a highly hydrostatic pressure transmitting medium allows for a clean simultaneous determination by a bulk probe of the antiferromagnetic and superconducting transitions. We compare our new phase diagram with the previous ones, discuss the nature (first or second order) of the various lines, and the coexistence of antiferromagnetic order and superconductivity. The link between the collaps of the superconducting heat anomaly and the broadening of the antiferromagnetic transition points to an inhomogeneous appearence of superconductivity below $P_c \approx 1.95$ GPa. Homogeneous bulk superconductivity is only observed above this critical pressure. We present a detailed analysis of the influence of pressure inomogeneities on the specific heat anomalies which emphasizes that the observed broadening of the transitions near $P_c$ is connected with the first order transition. For CeCoIn$_5$ we show that the large specific heat anomaly observed at $T_c$ at ambient pressure is suppressed linearly at least up to 3 GPa

Mutations in RAB39B Cause X-Linked Intellectual Disability and Early-Onset Parkinson Disease with alpha-Synuclein Pathology

Advances in understanding the etiology of Parkinson disease have been driven by the identification of causative mutations in families. Genetic analysis of an Australian family with three males displaying clinical features of early-onset parkinsonism and intellectual disability identified a approximately 45 kb deletion resulting in the complete loss of RAB39B. We subsequently identified a missense mutation (c.503C>A [p.Thr168Lys]) in RAB39B in an unrelated Wisconsin kindred affected by a similar clinical phenotype. In silico and in vitro studies demonstrated that the mutation destabilized the protein, consistent with loss of function. In vitro small-hairpin-RNA-mediated knockdown of Rab39b resulted in a reduction in the density of alpha-synuclein immunoreactive puncta in dendritic processes of cultured neurons. In addition, in multiple cell models, we demonstrated that knockdown of Rab39b was associated with reduced steady-state levels of alpha-synuclein. Post mortem studies demonstrated that loss of RAB39B resulted in pathologically confirmed Parkinson disease. There was extensive dopaminergic neuron loss in the substantia nigra and widespread classic Lewy body pathology. Additional pathological features included cortical Lewy bodies, brain iron accumulation, tau immunoreactivity, and axonal spheroids. Overall, we have shown that loss-of-function mutations in RAB39B cause intellectual disability and pathologically confirmed early-onset Parkinson disease. The loss of RAB39B results in dysregulation of alpha-synuclein homeostasis and a spectrum of neuropathological features that implicate RAB39B in the pathogenesis of Parkinson disease and potentially other neurodegenerative disorders

Superconducting and normal phases of FeSe single crystals at high pressure

We report on the synthesis of superconducting single crystals of FeSe, and their characterization by X-ray diffraction, magnetization and resistivity. We have performed ac susceptibility measurements under high pressure in a hydrostatic liquid argon medium up to 14 GPa and we find that TC increases up to 33-36 K in all samples, but with slightly different pressure dependences on different samples. Above 12 GPa no traces of superconductivity are found in any sample. We have also performed a room temperature high pressure X-ray diffraction study up to 12 GPa on a powder sample, and we find that between 8.5 GPa and 12 GPa, the tetragonal PbO structure undergoes a structural transition to a hexagonal structure. This transition results in a volume decrease of about 16%, and is accompanied by the appearance of an intermediate, probably orthorhombic phase

The peak in the thermal conductivity of Cu-O superconductors: Electronic or phononic origin?

The thermal conductivity К of hole-doped Cu-O plane high- T c perovskites exhibits a dramatic increase below T c which results in a pronounced peak near T c /2. The origin of this peak was initially thought to arise from an enhancement in the mean-free path of phonons as the charge carriers undergo condensation. Indeed, excellent fits to the data can be obtained with physically reasonable parameters using the conventional theory of lattice conduction in superconductors. In contrast, a recently observed sharp decrease in the quasiparticle scattering rate of YBCO single crystals below T c has motivated proposals for an electronic origin of the thermal conductivity peak. We shall critically examine experimental evidence and highlight relative advantages and shortcomings of the two contrasting interpretations. Furthermore, we shall draw attention to recently available data on the relaxation time of out-of-equilibrium carriers in Cu-O superconductors obtained using pump-probe femtosecond laser studies and what new light they shed on the controversy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45122/1/10948_2004_Article_BF00724562.pd

Thermal conductivity of high- T c superconductors

This paper reviews existing data on the thermal conductivity of high- T c superconductors. Included are discussions of pristine polycrystalline high- T c ceramics, single crystal specimens, and high- T c materials structurally modified by substitution or by radiation damage. The thermal conductivity of high- T c superconductors is compared with that of conventional superconductors, and dramatic differences are found between the two families. Mechanisms of thermal conductivity applicable to high- T c perovskites are discussed and implications for theories of high- T c superconductivity are noted.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45121/1/10948_2004_Article_BF00617463.pd