Discontinuous Almost Automorphic Functions and Almost Automorphic Solutions of Differential Equations with Piecewise Constant Argument

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental

Experimental Determination of Thermal Entanglement in Spin Clusters using Magnetic Susceptibility Measurements

The present work reports an experimental observation of thermal entanglement in a clusterized spin chain formed in the compound Na$_2$Cu$_5$Si$_4$O$_{14}$. The presence of entanglement was investigated through two measured quantities, an Entanglement Witness and the Entanglement of Formation, both derived from the magnetic susceptibility. It was found that pairwise entanglement exists below $\sim 200$ K. Tripartite entanglement was also observed below $\sim 240$ K. A theoretical study of entanglement evolution as a function of applied field and temperature is also presented.Comment: Submited to Phys. Rev.

Entanglement and Bell's inequality violation above room temperature in metal carboxylates

In the present work we show that a special family of materials, the metal carboxylates, may have entangled states up to very high temperatures. From magnetic susceptibility measurements, we have estimated the critical temperature below which entanglement exists in the cooper carboxylate \{Cu$_2$(O$_2$CH)$_4$\}\{Cu(O$_2$CH)$_2$(2-methylpyridine)$_2$\}, and we have found this to be above room temperature ($T_e \sim 630$ K). Furthermore, the results show that the system remains maximally entangled until close to $\sim 100$ K and the Bell's inequality is violated up to nearly room temperature ($\sim 290$ K)

Evidence for entanglement at high temperatures in an engineered molecular magnet

The molecular compound [Fe$_{2}$($\mu_{2}$-oxo)(C$_{3}$H$_{4}$N$_{2}$)$_{6}$(C$_{2}$O$_{4}$)$_{2}$] was designed and synthesized for the first time and its structure was determined using single-crystal X-ray diffraction. The magnetic susceptibility of this compound was measured from 2 to 300 K. The analysis of the susceptibility data using protocols developed for other spin singlet ground-state systems indicates that the quantum entanglement would remain at temperatures up to 732 K, significantly above the highest entanglement temperature reported to date. The large gap between the ground state and the first-excited state (282 K) suggests that the spin system may be somewhat immune to decohering mechanisms. Our measurements strongly suggest that molecular magnets are promising candidate platforms for quantum information processing

Substrate induced proximity effect in superconducting niobium nanofilms

Structural and superconducting properties of high quality Niobium nanofilms with different thicknesses are investigated on silicon oxide and sapphire substrates. The role played by the different substrates and the superconducting properties of the Nb films are discussed based on the defectivity of the films and on the presence of an interfacial oxide layer between the Nb film and the substrate. The X-ray absorption spectroscopy is employed to uncover the structure of the interfacial layer. We show that this interfacial layer leads to a strong proximity effect, specially in films deposited on a SiO$_2$ substrate, altering the superconducting properties of the Nb films. Our results establish that the critical temperature is determined by an interplay between quantum-size effects, due to the reduction of the Nb film thicknesses, and proximity effects

Immunity, Inflammation and Heart Failure: Their Role on Cardiac Function and Iron Status

Aims: Heart failure is a clinical syndrome characterized by subclinical systemic inflammation and immune system activation associated with iron deficiency. No data exist on the various activations of immune-mediated mechanisms of inflammation in heart failure patients with reduced/preserved ejection fraction. We aimed to (1) investigate possible differences in inflammatory parameters and oxidative stress, and (2) detect a different iron status between groups. Materials and Methods: We enrolled 50 consecutive Caucasian outpatients with heart failure. All patients underwent echocardiographic measurements, laboratory determinations, evaluation of iron status and Toll-like receptors, and NF-κB expression in peripheral blood mononuclear cells, as well as pro-inflammatory cytokines. All statistical calculations were made using SPSS for Mac version 21.0. Results: Patients with reduced ejection fraction showed significantly lower hemoglobin levels (12.3 ± 1.4 vs. 13.6 ± 1.4 g/dl), serum iron (61.4 ± 18.3 vs. 93.7 ± 33.7 mcg/dl), transferrin iron binding capacity (20.7 ± 8.4 vs. 31.1 ± 15.6 %), and e-GFR values (78.1 ± 36.1 vs. 118.1 ± 33.9 ml/min/1.73 m2) in comparison to patients with preserved ejection fraction, while unsaturated iron binding capacity (272.6 ± 74.9 vs. 221.7 ± 61.4 mcg/dl), hepcidin (4.61 ± 0.89 vs. 3.28 ± 0.69 ng/ml), and creatinine (1.34 ± 0.55 vs. 1.03 ± 0.25 mg/dl) were significantly higher in the same group. When considering inflammatory parameters, patients with reduced ejection fraction showed significantly higher expression of both Toll-like receptors-2 (1.90 ± 0.97 vs. 1.25 ± 0.76 MFI) and Toll-like receptors-4 (4.54 ± 1.32 vs. 3.38 ± 1.62 MFI), respectively, as well as a significantly higher activity of NF-κB (2.67 ± 0.60 vs. 1.07 ± 0.30). Furthermore, pro-inflammatory cytokines, interleukin-1, and interleukin-6, was significantly higher in patients with reduced ejection fraction, while the protective cytokine interleukin-10 was significantly lower in the same group. Correlational analyses demonstrated a significant and inverse relationship between left ventricular function and inflammatory parameters in patients with reduced ejection fraction, as well as a direct correlation between ferritin and inflammatory parameters. Conclusions: Our data demonstrate a different immune-mediated inflammatory burden in heart failure patients with reduced or preserved ejection fraction, as well as significant differences in iron status. These data contribute to further elucidate pathophysiologic mechanisms leading to cardiac dysfunction

Large classical universes emerging from quantum cosmology

It is generally believed that one cannot obtain a large Universe from quantum cosmological models without an inflationary phase in the classical expanding era because the typical size of the Universe after leaving the quantum regime should be around the Planck length, and the standard decelerated classical expansion after that is not sufficient to enlarge the Universe in the time available. For instance, in many quantum minisuperspace bouncing models studied in the literature, solutions where the Universe leave the quantum regime in the expanding phase with appropriate size have negligible probability amplitude with respect to solutions leaving this regime around the Planck length. In this paper, I present a general class of moving gaussian solutions of the Wheeler-DeWitt equation where the velocity of the wave in minisuperspace along the scale factor axis, which is the new large parameter introduced in order to circumvent the abovementioned problem, induces a large acceleration around the quantum bounce, forcing the Universe to leave the quantum regime sufficiently big to increase afterwards to the present size, without needing any classical inflationary phase in between, and with reasonable relative probability amplitudes with respect to models leaving the quantum regime around the Planck scale. Furthermore, linear perturbations around this background model are free of any transplanckian problem.Comment: 8 pages, 1 figur