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The spectrum and essential spectrum of the Dirichlet problem for an arbitrary elliptic operator with real constant coefficients are studied

Normal and uremic conscious rats that had been maintained on a low-protein diet were given oral protein or carbohydrate loads, and clearance studies were performed. Both the normal and uremic animals demonstrated a approximately 30% increase in glomerular filtration rate (GFR) in response to the protein bolus, but no significant increase in GFR was seen following the carbohydrate bolus. Similar studies were performed in uremic rats on a standard protein diet. The changes in GFR that were seen after an albumin bolus were similar but not as pronounced as those noted in the animals on the low-protein diet. Pretreatment with either aspirin or meclofenamate, cyclooxygenase inhibitors, completely blocked the protein-induced rise in GFR. The rats of glomerular production of prostaglandin (PG) E2 and 6-keto-PGF1 alpha (a stable metabolite of prostacyclin, PGI2) were determined by radioimmunoassay in a similar group of normal rats. The synthetic rates of PGE2 and 6-keto-PGF1 alpha following the protein bolus were 40 and 52% greater, respectively, than those observed following the carbohydrate load (P less than 0.005). Aspirin decreased glomerular prostanoid production in protein-treated animals by greater than 60%. Thus it appears that in the setting of protein restriction, the percent increase in GFR following a protein load is similar in both the normal and uremic rats, the increase in GFR in uremic rats is attenuated when animals were allowed to ingest a normal protein diet prior to study, and the increase in GFR seen in response to a protein load may be related to an increase in the synthesis of one or more vasodilatory glomerular prostanoids.

On donne des conditions qui assurent l'existence d'un nombre fini de valeurs propres sur la partie gauche de l'extremite du spectre essentiel

We prove that the minimal and maximal operators associated with an elliptic pseudodifferential operator coincide in L p ( R n ) , 1 > p > ∞ {L^p}({{\mathbf {R}}^n}),1 > p > \infty . We obtain a set of necessary and sufficient conditions for a measurable function q q on R n {{\mathbf {R}}^n} to be compact relative to some integral power of a constant coefficient elliptic pseudodifferential operator.

We describe the spectrum of a self-adjoint pseudo-differential operator on L2 (– ∞, ∞). We show that the essential spectrum coincides with the interval ([1, ∞) and give a lower bound for the lowest eigenvalue in (– ∞, 1). A sufficient condition for the existence of an eigenvalue in (– ∞, 1) is also given.

We give conditions on p and the symbol of a pseudo-differential operator such that the spectrum and essential spectrum of the operator on LP coincide with the range of the symbol.

In a 1928 paper [1], Hardy and Littlewood published the following inequality which is valid for all non-negative measurable functions ƒ and g on ( − ∞, ∞):where 1 < p, q < ∞, 0 < λ < 1, l/p + 1/q + λ = 2 and Cλp, q depends only on λ, p, q; ‖ƒ‖p and ‖g‖q are the Lp and Lq norms of ƒ and g respectively. See also p. 288 of the monograph [2] by Hardy, Littlewood and Pólya for a discussion of this inequality and related matters.

vibration and gives information on the relative importance of various elements to system stability. To eliminate the vibration, hydraulic accumulators were placed in the propellant suction lines near the pump inlets. This is shown schematically in the left fuel line in Fig. 2. The accumulator is a spring mass device that alters the dynamic characteristics of the suction line. By proper choice of accumulator constants, the propulsion system can effectively be decoupled from the structure. Mathematically, the accumulator is included in the model through the equation

The anticancer activities of beta-carotene, astaxanthin and canthaxanthin against the growth of mammary tumors were studied in female eight-wk-old BALB/c mice. The mice were fed a synthetic diet containing 0, 0.1 or 0.4% beta-carotene, astaxanthin or canthaxanthin. After 3 weeks, all mice were inoculated with 1 x 10(6) WAZ-2T tumor cells into the mammary fat pad. All animals were killed on 45 d after inoculation with the tumor cells. No carotenoids were detectable in the plasma or tumor tissues of unsupplemented mice. Concentrations of plasma astaxanthin (20 to 28 mumol/L) were greater (P0.05) than that of beta-carotene (0.1 to 0.2 mumol/L) and canthaxanthin (3 to 6 mmol/L). However, in tumor tissues, the concentration of canthaxanthin (4.9 to 6.0 nmol/g) was higher than that of beta-carotene (0.2 to 0.5 nmol/g) and astaxanthin (1.2 to 2.7 nmol/g). In general, all three carotenoids decreased mammary tumor volume. Mammary tumor growth inhibition by astaxanthin was dose-dependent and was higher than that of canthaxanthin and beta-carotene. Mice fed 0.4% beta-carotene or canthaxanthin did not show further increases in tumor growth inhibition compared to those fed 0.1% of each carotenoid. Lipid peroxidation activity in tumors was lower (P0.05) in mice fed 0.4% astaxanthin, but not in those fed beta-carotene and canthaxanthin. Therefore, beta-carotene, canthaxanthin and especially astaxanthin inhibit the growth of mammary tumors in mice; their anti-tumor activity is also influenced by the supplemental dose.

The 6th International Structural Engineering and Construction Conference (ISEC-6), Zurich, Switzerland, 21-26 June 2011.

International audience; As relevant in mineral exploration of the Earth using inductive electromagnetic means, (diffusive) scattering by a perfectly conducting ellipsoidal anomaly placed in a homogeneous conductive medium and illuminated by a time-harmonic magnetic dipole, is considered by means of a low frequency expansion in positive integral powers of (jk), k complex wavenumber of the exterior medium. The aim is to construct a simple yet robust model of the fields to identify the anomaly when magnetic fields are collected nearby. The approach is illustrated by field calculations and inversions of both synthetic and experimental data.