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

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

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

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

Miglioramento della resistenza e della performance muscolare mediante trattamento con onde d’urto defocalizzate

Scopo di questo studio \ue8 la valutazione degli effetti di un trattamento con onde d\u2019urto defocalizzate sull\u2019attivit\ue0 del muscolo scheletrico in termini di resistenza e di performance. Sono stati reclutati 60 soggetti sani, 30 maschi e 30 femmine. 40 pazienti sono stati sottoposti al protocollo di intervento, mentre 20 hanno partecipato al gruppo di controllo, senza ricevere il trattamento con onde d\u2019urto. Al termine di un ciclo di quattro sedute di onde d\u2019urto si \ue8 osservato un aumento dell\u2019Endurance Time e una diminuzione della Frequenza Cardiaca Massimale durante il test da sforzo a carico costante su cicloergometro. A 12 settimane dalla fine del trattamento i valori della Frequenza cardiaca Massimale non hanno subito variazioni statisticamente significative, mentre quelli dell\u2019Endurance Time hanno subito un ritorno ai valori basali. Per quanto riguarda la performance muscolare si \ue8 visto un miglioramento significativo alla valutazione T1, subito dopo la terapia con onde d\u2019urto, e alla valutazione T2, 12 settimane dopo l\u2019ultima seduta di onde d\u2019urto, rispetto alla valutazione iniziale a T0. Non \ue8 stata evidenziata una differenza statisticamente significativa tra i valori rilevati a T1e quelli a T2. I risultati di questo studio suggeriscono che il trattamento con onde d\u2019urto defocalizzate pu\uf2 portare a un miglioramento dell\u2019attivit\ue0 del muscolo scheletrico in termini di performance e di resistenza muscolare senza provocare alcun tipo di danno ai tessuti. Questi risultati aprono possibilit\ue0 di applicazione di questa metodica sia in ambito clinico (per esempio per il recupero funzionale dell\u2019amiotrofia ex non usu), sia in ambito sportivo

Income, Consumption and Remittances: Evidence from Immigrants to Australia

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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

Amount of substance and the mole in the SI

Abstract Following the revision of the International System of Units (SI), that takes effect on 20 May 2019, the unit mole is defined by using a fixed number of elementary entities. This number is the fixed numerical value of the Avogadro constant, which is the defining constant of the unit mole. This definition was made possible because the determination of the Avogadro constant had reached a level of relative uncertainty that allowed its value to be fixed and, at the same time, safeguard continuity of measurement results before and after the definition. The motivation for the revision of the SI and the mole in particular will be explained and the experimental work that allowed it is summarized

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

Qualitative Real-Time Schlieren and Shadowgraph Imaging of Human Exhaled Airflows: An Aid to Aerosol Infection Control

Using a newly constructed airflow imaging system, airflow patterns were visualized that were associated with common, everyday respiratory activities (e.g. breathing, talking, laughing, whistling). The effectiveness of various interventions (e.g. putting hands and tissues across the mouth and nose) to reduce the potential transmission of airborne infection, whilst coughing and sneezing, were also investigated. From the digital video footage recorded, it was seen that both coughing and sneezing are relatively poorly contained by commonly used configurations of single-handed shielding maneuvers. Only some but not all of the forward momentum of the cough and sneeze puffs are curtailed with various hand techniques, and the remaining momentum is disseminated in a large puff in the immediate vicinity of the cougher, which may still act as a nearby source of infection. The use of a tissue (in this case, 4-ply, opened and ready in the hand) proved to be surprisingly effective, though the effectiveness of this depends on the tissue remaining intact and not ripping apart. Interestingly, the use of a novel ‘coughcatcher’ device appears to be relatively effective in containing coughs and sneezes. One aspect that became evident during the experimental procedures was that the effectiveness of all of these barrier interventions is very much dependent on the speed with which the user can put them into position to cover the mouth and nose effectively