A conjectural extension of Hecke’s converse theorem

We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses

An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.Comment: 4 pages, 5 figures, 3 table

Pinus mugo essential oil impairs STAT3 activation through oxidative stress and induces apoptosis in prostate cancer cells

Essential oils (EOs) and their components have been reported to possess anticancer properties and to increase the sensitivity of cancer cells to chemotherapy. The aim of this work was to select EOs able to downregulate STAT3 signaling using Western blot and RT-PCR analyses. The molecular mechanism of anti-STAT3 activity was evaluated through spectrophotometric and fluorometric analyses, and the biological effect of STAT3 inhibition was analyzed by flow cytometry and wound healing assay. Herein, Pinus mugo EO (PMEO) is identified as an inhibitor of constitutive STAT3 phosphorylation in human prostate cancer cells, DU145. The down-modulation of the STAT3 signaling cascade decreased the expression of anti-proliferative as well as anti-apoptotic genes and proteins, leading to the inhibition of cell migration and apoptotic cell death. PMEO treatment induced a rapid drop in glutathione (GSH) levels and an increase in reactive oxygen species (ROS) concentration, resulting in mild oxidative stress. Pretreatment of cells with N-acetyl-cysteine (NAC), a cell-permeable ROS scavenger, reverted the inhibitory action of PMEO on STAT3 phosphorylation. Moreover, combination therapy revealed that PMEO treatment displayed synergism with cisplatin in inducing the cytotoxic effect. Overall, our data highlight the importance of STAT3 signaling in PMEO cytotoxic activity, as well as the possibility of developing adjuvant therapy or sensitizing cancer cells to conventional chemotherapy

Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems

A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view, the two phases are characterized by two distinct single-particle motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous diffusion is observed up to a time $\tau$ that increases linearly with $N$. Therefore, the finite particle number acts like a white noise source for the system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review

Intraoperative Defibrillation Testing of Subcutaneous Implantable Cardioverter‐Defibrillator Systems—A Simple Issue?

Background: The results of the recently published randomized SIMPLE trial question the role of routine intraoperative defibrillation testing. However, testing is still recommended during implantation of the entirely subcutaneous implantable cardioverter‐defibrillator (S‐ICD) system. To address the question of whether defibrillation testing in S‐ICD systems is still necessary, we analyzed the data of a large, standard‐of‐care prospective single‐center S‐ICD registry. // Methods and Results: In the present study, 102 consecutive patients received an S‐ICD for primary (n=50) or secondary prevention (n=52). Defibrillation testing was performed in all except 4 patients. In 74 (75%; 95% CI 0.66–0.83) of 98 patients, ventricular fibrillation was effectively terminated by the first programmed internal shock. In 24 (25%; 95% CI 0.22–0.44) of 98 patients, the first internal shock was ineffective and further internal or external shock deliveries were required. In these patients, programming to reversed shock polarity (n=14) or repositioning of the sensing lead (n=1) or the pulse generator (n=5) led to successful defibrillation. In 4 patients, a safety margin of <10 J was not attained. Nevertheless, in these 4 patients, ventricular arrhythmias were effectively terminated with an internal 80‐J shock. // Conclusions: Although it has been shown that defibrillation testing is not necessary in transvenous ICD systems, it seems particular important for S‐ICD systems, because in nearly 25% of the cases the primary intraoperative test was not successful. In most cases, a successful defibrillation could be achieved by changing shock polarity or by optimizing the shock vector caused by the pulse generator or lead repositioning.<br

Equilibrium and dynamical properties of two dimensional self-gravitating systems

A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously distributed. A phase transition from the collapsed to the homogeneous state occurs at critical energy U_c. A theoretical analysis within the canonical ensemble identifies such a transition as first order. But microcanonical simulations reveal a negative specific heat regime near $U_c$. The dynamical behaviour of the system is affected by this transition : below U_c anomalous diffusion is observed, while for U > U_c the motion of the particles is almost ballistic. In the collapsed phase, finite $N$-effects act like a noise source of variance O(1/N), that restores normal diffusion on a time scale diverging with N. As a consequence, the asymptotic diffusion coefficient will also diverge algebraically with N and superdiffusion will be observable at any time in the limit N \to \infty. A Lyapunov analysis reveals that for U > U_c the maximal exponent \lambda decreases proportionally to N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy, in spite of a clear non ergodicity of the system, a common scaling law \lambda \propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two column version with included figures : less paper waste

Improved measurement results for the Avogadro constant using a 28Si-enriched crystal

New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of $N_A = 6.022 140 76(12) \times 10^{23}$ mol$^{-1}$. The X-ray crystal density method has thus achieved the target relative standard uncertainty of $2.0 \times 10^{-8}$ necessary for the realization of the definition of the new kilogram.Comment: postprint, 22 page, 3 figures, 14 table

A new generation of 99.999% enriched 28Si single crystals for the determination of Avogadro's constant

A metrological challenge is currently underway to replace the present definition of the kilogram. One prerequisite for this is that the Avogadro constant, NA, which defines the number of atoms in a mole, needs to be determined with a relative uncertainty of better than 2  ×  10−8. The method applied in this case is based on the x-ray crystal density experiment using silicon crystals. The first attempt, in which silicon of natural isotopic composition was used, failed. The solution chosen subsequently was the usage of silicon highly enriched in 28Si from Russia. First, this paper reviews previous efforts from the very first beginnings to an international collaboration with the goal of producing a 28Si single crystal with a mass of 5 kg, an enrichment greater than 0.9999 and of sufficient chemical purity. Then the paper describes the activities of a follow-up project, conducted by PTB, to produce a new generation of highly enriched silicon in order to demonstrate the quasi-industrial and reliable production of more than 12 kg of the 28Si material with enrichments of five nines. The intention of this project is also to show the availability of 28Si single crystals as a guarantee for the future realisation of the redefined kilogram

Income, Consumption and Remittances: Evidence from Immigrants to Australia

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