On the index of elliptic partial differential operators inR n

Summary Let A= be an elliptic differential operator inR _u, If, for |α|=l, the coefficients a_α are ? nearly constant ? and, for |α|<l, they tend to zero at infinity with a certain swiftness, it is proved that A is a Fredholm operator with index_x(A)=0 between a suitable weighted Sobolev space M contained in W^l,p (R n) and L^p(R ⁿ, (1+|x|)^lp)== . It is shown, by counterexamples, that the above result, holds only if n>l, p>n/(n−l) and that isomorphism results can be obtained, in general only if the coefficients a_α(|α|<l) are assumed to be ? sufficiently small ? also on compact sets. Then a Sturm-Liouville type problem is studied and a class of negative and falling off at infinity potentials V(x) is constructed in such a way that the Schr?dinger operator H=−Δ+V(x), in L²(R ⁿ), has a zero eigenvalue.

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Sunto Sia un operatore differenziale ellittico inR ⁿ. Se, per |α|=l, i coefficienti a_α sono ? quasi costanti ? e, per |α|<l, tendono a zero all'infinito con una certa rapidità, si dimostra che A è un operatore di Fredholm con indice_X(A)=0 tra un opportuno spazio di Sobolev con peso M contenuto in W^l,p(R ⁿ) ed L^p(R ⁿ, (1+|x|)^lp)== . Si prova, mediante controesempi, che tale risultato è valido solo se n>l, p>n/(n−l) e che teoremi di isomorfismo si possono ottenere, in generale, solo se si assume che i coefficienti a_α (|α|<l) sono ? sufficientemente piccoli ? anche su insiemi compatti. Si studia quindi un problema del tipo Sturm-Liouville e si costruisce una classe di potenziali V(x) negativi e convergenti a zero all'infinito, tali che l'operatore di Schr?dinger H=−δ+V(x) in L²(R ⁿ) abbia un autovalore nullo.

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Entrata in Redazione il 10 agosto 1977.

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Work supported by C.N.R. (G.N.A.F.A.).     

Recent advances in electrochemical water technologies for the treatment of antibiotics: A short review

This short review presents a critical overview of the most recent works published in the literature related to the use of electrochemical advanced oxidation processes (EAOPs) for the treatment of antibiotics present in synthetic and real wastewaters. The first section focuses on novelties within the traditional EAOPs, including electrochemical oxidation and electrochemical Fenton-based processes. The second section is devoted to new electrochemical technologies, including heterogeneous electro-Fenton, electrochemically activated persulfate processes, and combined processes. Future perspectives about these processes are also presented to aid the continuous evolution of research in the area.     

Experimental implementation of a concatenated quantum error-correcting code

Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information processing. We report the implementation of a concatenated quantum error-correcting code able to correct phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error correction is a practical tool to handle realistic noise involving both independent and correlated errors.     

Carrier trapping in thin N2O-grown oxynitride/oxide di-layer for PowerMOSFET devices

A detailed study of the carrier trapping properties shown by the silicon/oxynitride/oxide gate layers in PowerVDMOS technologies is reported. A quantitative analysis of hole and electron trap densities versus the specific N₂O based nitridation process, extracted from Fowler–Nordheim constant current stress kinetics, allows a deep understanding of the role played by those defects in the susceptibility of every nitrided layer.     

A study on shielding gas contamination in laser welding of non-ferrous alloys

Laser welding of non-ferrous alloys is a high-productivity and cost-effective joining technology, which gained an undoubted interest especially in aerospace, chemical and medical industry, where high strength and corrosion resistant mechanical parts are required. Unfortunately some of the most used non-ferrous alloys are highly reactive with respect to the components of the environmental atmosphere: oxygen, nitrogen, hydrogen and humidity. This reactivity leads to the formation of porosities and to oxides and nitrides inclusion, which are responsible for a decrease of ductility and strength in welded joints.According to this a good shielding technique of the weld pool is of primary importance in order to obtain sound beads and reliable manufacturings. This paper deals with the opportunity of simulating the shielding gas behavior by means of Computational Fluid Dynamics software in order to understand the relationship among the outlet position, the shielding gas type and its flow rate.A simulation activity was carried out in order to evaluate the behavior of shielding gas concentration surrounding the weld pool. The simulated welding environment was simplified without considering the presence and the effect of the plasma plume. The main results concern the shielding gas contamination prediction with respect to the distance from the beam-material interaction zone.     

Polysilicon TFT structures for kink-effect suppression

Experimental results and numerical simulations of asymmetric fingered polysilicon thin-film transistors (AF-TFTs) are analyzed in detail. In the AF-TFTs, the transistor channel region is split into two zones with different lengths separated by a floating n/sup +/ region. This structure allows an effective reduction of the kink effect depending on the relative length of the two subchannels, without introducing any additional series resistance. In addition, an appreciable reduction of the leakage current is also observed. The AF-TFTs characteristics have been analyzed by two-dimensional numerical simulation and by modeling the device with two transistors in series. This model clarifies the mechanisms of kink effect suppression in AF-TFT. On the basis of this analysis, two new modified device structures for kink-effect suppression are also proposed and discussed.     

Electronics with and on paper

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Interface states and traps in thin N2O-grown oxynitride/oxide di-layer for PowerMOSFET devices

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Scaling and universality in proportional elections

A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavor is to find regularities in data referring to large-scale social phenomena, such as scaling and universality. We show that, in proportional elections, the distribution of the number of votes received by candidates is a universal scaling function, identical in different countries and years. This finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical, political, and/or economical context where voters operate. A simple dynamical model for the behavior of voters, similar to a branching process, reproduces the universal distribution.