Elliptic Equations with Degenerate Coercivity： Gradient Regularity

In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is where for example, a(x,u)=(1+|u|)^−θ with θ ∈ (0,1). We study the same problem for minima of functionals closely related to the previous equation.     

Asymptotic behavior of solutions of variational equations

In questo articolo si considerano equazioni differenziali ordinarie del secondo ordine della forma $$\{ A(u')u'\} ' + \delta (r)A(u')u' + f(r,u) = 0,$$ dove cioè la nonlinearità è presente sia nella variabile soluzioneu che nella sua derivata. Si forniscono proprietà di monotonia, oscillazione e un accurato studio del comportamento asintotico all’ infinito delle soluzioni, quandoA, δ,f hanno crescite asintotiche di tipo algebrico.     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

Probabilistically induced domain decomposition methods for elliptic boundary-value problems

Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few interfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to split the original problem into fully decoupled subproblems. The numerical treatment can then be continued, implementing any deterministic algorithm on each subdomain. Both, Monte Carlo (or quasi-Monte Carlo) simulations and the domain decomposition strategy allow for exploiting parallel architectures. Scalability and natural fault tolerance are peculiarities of the present algorithm. Examples concern Helmholtz and Poisson equations, whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source.     

Characterization of CaTi0.9Fe0.1O3/La0.98Mg0.02NbO4 composite

A composite of CaTi_0.9Fe_0.1O₃ and electrolyte material, i.e. magnesium doped La_0.98Mg_0.02NbO₄ was prepared and studied. The phase content and the sample microstructure was examined by an X-ray diffraction method and scanning electron microscopy. EDS measurements were done both for composite samples and the diffusion couple. The electrical properties were studied by four terminal DC method. The high-temperature interaction between the two components of the composite has been observed. It has been suggested that lanthanum diffused into the perovskite phase and substituted for calcium whereas calcium and niobium formed the Ca₂Nb₂O₇ pyrochlore phase. At 1500°C very large crystallites of the pyrochlore were observed. Regardless of strong interaction between the composite components, its total conductivity was weakly dependent on the sintering temperature.     

A longitudinal study of MR diffusion changes in normal appearing white matter of patients with early multiple sclerosis

BACKGROUND AND PURPOSE: The stage at which normal appearing white matter (NAWM) abnormalities first appear in multiple sclerosis (MS) is not clear. The aim of our study was to monitor water diffusion changes over time in NAWM of patients with early MS.METHODS: Out of a consecutive series of patients enrolled in a MR study on clinically isolated syndrome (CIS), we selected 19 subjects who had completed a one year follow-up. The MR scans obtained at baseline and at 12 months were reviewed according to the new criteria on the diagnosis of MS. Lesion load on T2 and T1 weighted images and the trace of the apparent diffusion coefficient in NAWM were measured both at baseline and at 12 months in patients and in 12 healthy controls.RESULTS: In three patients the diagnosis of MS was done at baseline based on MR. Thirteen patients developed MS during the study and in three patients the diagnosis remained "possible MS." TADC in NAWM in patients was significantly higher than in controls at the 12 months' follow-up but not at baseline (controls mean tADC +/- sd = 0.745 +/- 0.02 mm(2)/sec x 10(-3); patients mean tADC(12) +/- sd = 0.767 +/- 0.02 mm(2)/sec x 10(-3); p < 0.02). TADC and T2 lesion load at 12 months were significantly correlated (p < 0.01). Patients exhibiting tADC(12) above a confidence interval had a significantly greater EDSS score at the same time period (EDSS(12) +/- sd = 1.9 +/- 0.5 and = 1.1 +/- 0.4 respectively; p < 0.01).CONCLUSIONS: This study suggests that diffusion MR cannot detect alterations in NAWM of patients with a CIS suggestive of MS. After one year, when most patients develop MS, diffusion MR abnormalities in NAWM become apparent. These abnormalities are correlated with T2 lesion load and may contribute to neurological impairment.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

Bibliometric Analysis on Supercritical CO2 Power Cycles for Concentrating Solar Power Applications

In recent years, supercritical CO₂ power cycles have received a large amount of interest due to their exceptional theoretical conversion efficiency above 50%, which is leading a revolution in power cycle research. Furthermore, this high efficiency can be achieved at a moderate temperature level, thus suiting concentrating solar power (CSP) applications, which are seen as a core business within supercritical technologies. In this context, numerous studies have been published, creating the need for a thorough analysis to identify research areas of interest and the main researchers in the field. In this work, a bibliometric analysis of supercritical CO₂ for CSP applications was undertaken considering all indexed publications within the Web of Science between 1990 and 2020. The main researchers and areas of interest were identified through network mapping and text mining techniques, thus providing the reader with an unbiased overview of sCO₂ research activities. The results of the review were compared with the most recent research projects and programs on sCO₂ for CSP applications. It was found that popular research areas in this topic are related to optimization and thermodynamics analysis, which reflects the significance of power cycle configuration and working conditions. Growing interest in medium temperature applications and the design of sCO₂ heat exchangers was also identified through density visualization maps and confirmed by a review of research projects.