On fewnomials, integral points and a toric version of Bertini's theorem

An old conjecture of Erdős and Rényi, proved by Schinzel, predicted a bound for the number of terms of a polynomial g(x)∈ℂ[x] when its square g(x)² has a given number of terms. Further conjectures and results arose, but some fundamental questions remained open. In this paper, with methods which appear to be new, we achieve a final result in this direction for completely general algebraic equations f(x,g(x))=0, where f(x,y) is monic of arbitrary degree in y, and has boundedly many terms in x: we prove that the number of terms of such a g(x) is necessarily bounded. This includes the previous results as extremely special cases. We shall interpret polynomials with boundedly many terms as the restrictions to 1-parameter subgroups or cosets of regular functions of bounded degree on a given torus Glm. Such a viewpoint shall lead to some best-possible corollaries in the context of finite covers of Glm, concerning the structure of their integral points over function fields (in the spirit of conjectures of Vojta) and a Bertini-type irreducibility theorem above algebraic multiplicative cosets. A further natural reading occurs in non-standard arithmetic, where our result translates into an algebraic and integral-closedness statement inside the ring of non-standard polynomials

Polynomial–exponential equations and Zilber's conjecture

Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtain the result by proving (unconditionally) that certain polynomial–exponential equations have only finitely many rational solutions. This answers affirmatively a question of David Marker, who asked, and proved in the case of algebraic coefficients, whether at least the one variable case of Zilber's strong exponential-algebraic closedness conjecture can be reduced to Schanuel's conjecture

Characterization and BMP Tests of Liquid Substrates for High-rate Anaerobic Digestion

This work was focused on the physicochemical characterization and biochemical methane potential (BMP) tests of some liquid organic substrates, to verify if they were suitable for undergoing a process of high-velocity anaerobic digestion. The selected substrates were: first and second cheese whey, organic fraction of municipal solid waste (OFMSW) leachate, condensate water and slaughterhouse liquid waste. Firstly, a physicochemical characterization was performed, using traditional and macromolecular parameters; then, batch anaerobic tests were carried out, and some continuous tests were planned. The results revealed that all the analyzed substrates have a potential to be anaerobically treated. Valuable information about treatment rate for a high-velocity anaerobic digestion process was obtained. Start-up of a lab-scale UASB reactor, treating diluted cheese whey, was successfully achieved with good COD removal efficiency. These preliminary results are expected to be further investigated in a successive phase, where continuous tests will be conducted on condensate water and OFMSW leachate. This work is licensed under a Creative Commons Attribution 4.0 International License

Calibration-Free and High-Sensitivity Microwave Detectors Based on InAs/InP Nanowire Double Quantum Dots

At the cutting-edge of microwave detection technology, novel approaches which exploit the interaction between microwaves and quantum devices are rising. In this study, microwaves are efficiently detected exploiting the unique transport features of InAs/InP nanowire double quantum dot-based devices, suitably configured to allow the precise and calibration-free measurement of the local field. Prototypical nanoscale detectors are operated both at zero and finite source-drain bias, addressing and rationalizing the microwave impact on the charge stability diagram. The detector performance is addressed by measuring its responsivity, quantum efficiency and noise equivalent power that, upon impedance matching optimization, are estimated to reach values up to approximate to 2000 A W-1, 0.04 and root HZ, respectively. The interaction mechanism between the microwave field and the quantum confined energy levels of the double quantum dots is unveiled and it is shown that these semiconductor nanostructures allow the direct assessment of the local intensity of the microwave field without the need for any calibration tool. Thus, the reported nanoscale devices based on III-V nanowire heterostructures represent a novel class of calibration-free and highly sensitive probes of microwave radiation, with nanometer-scale spatial resolution, that may foster the development of novel high-performance microwave circuitries

Growth of self-catalyzed inas/insb axial heterostructured nanowires: Experiment and theory

The growth mechanisms of self-catalyzed InAs/InSb axial nanowire heterostructures are thoroughly investigated as a function of the In and Sb line pressures and growth time. Some interesting phenomena are observed and analyzed. In particular, the presence of In droplet on top of InSb segment is shown to be essential for forming axial heterostructures in the self-catalyzed vapor-liquid-solid mode. Axial versus radial growth rates of InSb segment are investigated under different growth conditions and described within a dedicated model containing no free parameters. It is shown that widening of InSb segment with respect to InAs stem is controlled by the vapor-solid growth on the nanowire sidewalls rather than by the droplet swelling. The In droplet can even shrink smaller than the nanowire facet under Sb-rich conditions. These results shed more light on the growth mechanisms of self-catalyzed heterostructures and give clear route for engineering the morphology of InAs/InSb axial nanowire heterostructures for different applications

Morphology control of single-crystal InSb nanostructures by tuning the growth parameters

Research interest in indium antimonide (InSb) has increased significantly in recent years owing to its intrinsic properties and the consequent opportunities to implement next-generation quantum devices. Hence, the precise, reproducible control over morphology and crystalline quality becomes of paramount importance for a practical quantum-device technology. Here, we investigate the growth of InSb nanostructures with different morphologies on InAs stems without pre-growth efforts (patterning). InSb nanostructures such as nanowires (1D), nanoflags (2D) and nanocubes (3D) have been realized by means of Au-assisted chemical beam epitaxy by tailoring the growth parameters like growth temperature, precursor fluxes, sample rotation and substrate orientation. Through morphological and crystallographic characterization, all the as-grown InSb 2D nanostructures are found to be single-crystalline with zinc blende structure, free from any defects such as stacking faults and twin planes. The existence of two families of 2D nanostructures, characterised by an aperture angle at the base of 145 and 160 , is observed and modelled. This study provides useful guidelines for the controlled growth of high-quality InSb nanostructures with different shape

Microwave-Assisted Tunneling in Hard-Wall InAs/InP Nanowire Quantum Dots

With downscaling of electronic circuits, components based on semiconductor quantum dots are assuming increasing relevance for future technologies. Their response under external stimuli intrinsically depend on their quantum properties. Here we investigate single-electron tunneling in hard-wall InAs/InP nanowires in the presence of an off-resonant microwave drive. Our heterostructured nanowires include InAs quantum dots (QDs) and exhibit different tunnel-current regimes. In particular, for source-drain bias up to few mV Coulomb diamonds spread with increasing contrast as a function of microwave power and present multiple current polarity reversals. This behavior can be modelled in terms of voltage fluctuations induced by the microwave field and presents features that depend on the interplay of the discrete energy levels that contribute to the tunneling process

Real-Time TDM-based optimization of continuous-infusion meropenem for improving treatment outcome of febrile neutropenia in oncohaematological patients: Results from a prospective, monocentric, interventional study

Objectives: To assess the role that real-Time therapeutic drug monitoring (TDM)-guided optimization of continuous-infusion (CI) meropenem may have in maximizing empirical treatment and in preventing breakthrough infection and/or colonization with carbapenem-resistant Enterobacteriaceae (CRE) among oncohaematological patients with febrile neutropenia (FN). Methods: A monocentric, interventional, prospective study was conducted. The pharmacodynamic (PD) target was a steady-state meropenem concentration-To-MIC ratio (Css/MIC) of 4-8. The primary endpoint was 14 day all-cause mortality. The secondary endpoint was the prevalence of CRE colonization in rectal swabs of patients rehospitalized within 3months. Results: Among the 75 patients enrolled, most (56%) had AML, almost half (37/75, 49.3%) underwent HSCT and one-Third (32%) received meropenem as monotherapy. Meropenem dosages were adjusted in 30.1% of TDM reassessments. Gram-negative infections were microbiologically documented in 20.0% of patients. All of the 12 patients having infections caused by in vitro meropenem-susceptible pathogens attained the desired PD target and were cured. Three patients had infections caused by in vitro meropenem-resistant pathogens. Two of these achieved a Css/MIC target of 1 and were cured; the other one achieved a suboptimal PD target (0.59) and died. The 14 day all-cause mortality (10.7%) was significantly associated, at multivariate regression, with HSCT (OR 0.086, 95% CI 0.008-0.936, P = 0.044) and with augmented renal clearance (OR 10.846, 95% CI 1.534-76.672, P = 0.017). None of the patients who had hospital readmissions in the 3month follow-up (63/75) had CRE colonization in rectal swabs. Conclusions: Real-Time TDM-guided CI meropenem may be a useful approach for attaining adequate exposure and preventing CRE emergence in FN oncohaematological patients