The method of interpolating integral equations for quantum Fluids.—III

Summary A method for interpolating between the (F)HNC and (F)PY approaches in order to take into account elementary contributions has been presented in two preceding papers concerned with the properties of zero-temperature quantum fluids, described by short-range correlated wave functions. In the present paper, both for Bose and for Fermi systems, the technique is extended to the case in which the two-body radial distribution function contains a long-range tail, going asr ⁻⁴. The results obtained for the energy per particle and momentum distribution of liquid⁴He, polarized hydrogen and³He are presented in correspondence to variational wave functions containing only two-particle correlations.

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Riassunto In due precedenti lavori è stata sviluppata una tecnica di interpolazione tra le approssimazioni (F)HNC e (F)PY per tenere conto dei cosiddetti contributi elementari nel calcolo delle proprietà dei fluidi quantistici a temperatura zero e descritti da funzioni d’onda con fattori di correlazione a corto raggio. Nel presente lavoro il metodo è esteso, per sistemi sia bosonici che fermionici, al caso in cui la funzione radiale di distribuzione contenga una coda con andamentor ⁻⁴. Sono presentati i risultati ottenuti per l’energia per particella e la distribuzione di quantità di moto dell’⁴He liquido, dell’idrogeno polarizzato e dell’³He liquido, in corrispondenza a funzioni d’onda variazionali contenenti solo correlazioni di coppia.

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Резюме В двух предыдущих работах был предложен метод интерполяции между (F)HNC и (F)PY подходами. В этих работах рассматривались свойства квантовых жидкостей при нулевой температуре, которые описываются волновыми функциями с короткодействующими корреляциями. В данной работе, для Бозеи Ферми-систем, предложенная тенхика обобщается на случай, когда двух-частичная радиальная функция распределения содержит длиннодействующий хвост, который спадает какr ⁻⁴. Приводятся результаты для энергии на одну частицу и импульсное распределение для жидкого⁴He, поляризованного водорода и³H, причем соответствующие вариационные волновые функции содержат только двух-частичные корреляции.

     

Ideals of varieties parameterized by certain symmetric tensors

The ideal of a Segre variety P^n₁×?×P^n_t?P^{(n₁+1)?(n_t+1)−1} is generated by the 2-minors of a generic hypermatrix of indeterminates (see [H.T. Hà, Box-shaped matrices and the defining ideal of certain blowup surface, J. Pure Appl. Algebra 167 (2-3) (2002) 203-224. MR1874542 (2002h:13020)] and [R. Grone, Decomposable tensors as a quadratic variety, Proc. Amer. Math. 43 (2) (1977) 227-230. MR0472853 (57 #12542)]). We extend this result to the case of Segre-Veronese varieties. The main tool is the concept of “weak generic hypermatrix” which allows us to treat also the case of projection of Veronese surfaces from a set of general points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension 2.     

Commutators of fractional integral operators on Vanishing-Morrey spaces

In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey spaces VL ^p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal function and the fractional maximal function and related Morrey inequalities.      

Determination of Picoxystrobin and Pyraclostrobin by MEKC with On-Line Analyte Concentration

Micellar electrokinetic capillary chromatography was used for the determination of picoxystrobin and pyraclostrobin. The background electrolyte consisted of borate buffer (40 mmol L⁻¹ pH 8.5), SDS (30 mmol L⁻¹) and acetonitrile (15% in volume). Runs were made at 25 °C with 25 kV applied potential. The developed method was applied to analyte fortified urine samples. On-line analyte concentration, combined with a capillary of a longer optical path length, allowed limits of quantification of 8.6 × 10⁻⁸ mol L⁻¹ for picoxystrobin and 1.8 × 10⁻⁷ mol L⁻¹ for pyraclostrobin.

     

Photodegradation of the pharmaceuticals amoxicillin, bezafibrate and paracetamol by the photo-Fenton process—Application to sewage treatment plant effluent

Photodegradation of the pharmaceuticals amoxicillin (AMX), bezafibrate (BZF) and paracetamol (PCT) in aqueous solutions via the photo-Fenton process was investigated under black-light and solar irradiation. The influences of iron source, initial H₂O₂ concentration and matrix (distilled water and sewage treatment plant effluent) on degradation efficiency were discussed in detail. The results showed that (i) the degradation of the drugs was favored in the presence of potassium ferrioxalate (FeOx) in comparison to Fe(NO₃)₃; (ii) the increase of the H₂O₂ concentration improved the efficiency of AMX and BZF oxidation; however, the same was not observed for PCT; (iii) the influence of the matrix was observed for the degradation of BZF and PCT; (iv) under solar irradiation, the oxidation of the BZF and PCT is faster than under black-light irradiation. All these pharmaceuticals can be efficiently degraded employing the process evaluated.     

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.