SOME REMARKS ON THE SMARANDACHE FUNCTION

Remarks on a Function in the Number Theory

Polaron to molecule transition in a strongly imbalanced Fermi gas

A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wavefunction in the molecular limit, we determine the critical value for the polaron to molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et. al. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron to molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance.Comment: 10 pages, 4 figures, RevTex4, minor changes, references adde

Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasi-crystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry protected topological phases.Comment: 27 pages + 11 pages appendices. v3 Published version, with expanded discussion on a few point

On a modular property of N=2 superconformal theories in four dimensions

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure

Electrochemistry at nanoscale electrodes : individual single-walled carbon nanotubes (SWNTs) and SWNT-templated metal nanowires

Individual nanowires (NWs) and native single-walled carbon nanotubes (SWNTs) can be readily used as well-defined nanoscale electrodes (NSEs) for voltammetric analysis. Here, the simple photolithography-free fabrication of submillimeter long Au, Pt, and Pd NWs, with sub-100 nm heights, by templated electrodeposition onto ultralong flow-aligned SWNTs is demonstrated. Both individual Au NWs and SWNTs are employed as NSEs for electron-transfer (ET) kinetic quantification, using cyclic voltammetry (CV), in conjunction with a microcapillary-based electrochemical method. A small capillary with internal diameter in the range 30–70 μm, filled with solution containing a redox-active mediator (FcTMA+ ((trimethylammonium)methylferrocene), Fe(CN)64–, or hydrazine) is positioned above the NSE, so that the solution meniscus completes an electrochemical cell. A 3D finite-element model, faithfully reproducing the experimental geometry, is used to both analyze the experimental CVs and derive the rate of heterogeneous ET, using Butler–Volmer kinetics. For a 70 nm height Au NW, intrinsic rate constants, k0, up to ca. 1 cm s–1 can be resolved. Using the same experimental configuration the electrochemistry of individual SWNTs can also be accessed. For FcTMA+/2+ electrolysis the simulated ET kinetic parameters yield very fast ET kinetics (k0 > 2 ± 1 cm s–1). Some deviation between the experimental voltammetry and the idealized model is noted, suggesting that double-layer effects may influence ET at the nanoscale

Effectiveness and Overall Safety of NutropinAq (R) for Growth Hormone Deficiency and Other Paediatric Growth Hormone Disorders: Completion of the International Cooperative Growth Study, NutropinAq (R) European Registry (iNCGS)

Objective: The International Cooperative Growth Study, NutropinAq® European Registry (iNCGS) (NCT00455728) monitored long-term safety and effectiveness of recombinant human growth hormone (rhGH; NutropinAq® [somatropin]) in paediatric growth disorders. Methods: Open-label, non-interventional, post-marketing surveillance study recruiting children with growth disorders. Endpoints included gain in height standard deviation score (SDS), adult height, and occurrence of adverse events (AEs). Results: 2792 patients were enrolled. 2082 patients (74.6%) had growth hormone deficiency (GHD), which was isolated idiopathic in 1825 patients (87.7%). Non-GHD diagnoses included Turner syndrome (TS) (n=199), chronic renal insufficiency (CRI) (n=10), other non-GHD (n=498), and missing data for three participants. Improvements from baseline height SDS occurred at all time points to Month 132, and in all subgroups by disease aetiology. At Month 12, mean (95% CI) change in height SDS by aetiology was: idiopathic GHD 0.63 (0.61;0.66), organic GHD 0.71 (0.62;0.80), TS 0.59 (0.53; 0.65), CRI 0.54 (-0.49;1.56), and other non-GHD 0.64 (0.59;0.69). Mean height ( ± SD) at the last visit among the 235 patients with adult or near-adult height recorded was 154.0 cm ( ± 8.0) for girls and 166.7 cm ( ± 8.0) for boys. The most frequent biological and clinical non-serious drug-related AEs were increased insulin-like growth factor concentrations (314 events) and injection site haematoma (99 events). Serious AEs related to rhGH according to investigators were reported (n=30); the most frequent were scoliosis (4 events), epiphysiolysis (3 events), and strabismus (2 events). Conclusions: There was an improvement in mean height SDS in all aetiology subgroups after rhGH treatment. No new safety concerns were identified