Decay Estimates for Solutions of Porous Medium Equations with Advection

In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form

$$ u_{t} + \operatorname{div}f(x,t,u) = \operatorname{div}\bigl( |u|^{\alpha } \nabla u\bigr), \quad x \in \mathbb{R}^{n} , \ t > 0, $$

where \(\alpha > 0 \) is constant, decrease to zero, under fairly broad conditions on the advection flux \(f\). Besides that, we derive a time decay rate for these solutions.

     

Chemical reducing pedoenvironment in a peatland influenced by hematitic phyllite lithology in the southern Espinhaço chain,Brazil

A peatland in Pinheiro, Diamantina City, Minas Gerais State - Brazil, was sampled at different depths of two profiles with diverse vegetation coverings (grassland field and bush) in order to collect materials that might reflect changes in the chemical states of iron over the peat formation coming from original minerals such as hematitic phyllite surrounding the boggy pedon. Samples collected were chemically, structurally and magnetically characterized. The results show that both series of peats are composed of organic matter and minerals such as quartz, kaolinite, gibbsite, rutile and muscovite. Deeper layers present only quartz. Mössbauer spectroscopy shows that iron is present in both electron states, Fe²⁺ and Fe³⁺, under both vegetations, each valence appearing in the spectra in the form of a discrete doublet. No hyperfine magnetic splitting was observed in any spectrum at room temperature. The Mössbauer subspectral area of Fe²⁺ tended to increase from the upper to deeper layers. Magnetic measurements reveal that the magnetic response of the surface samples is the highest, displaying a sharp decrease below 15 cm and that the magnetic signal is a superposition of (super)paramagnetic and ferrimagnetic contributions. Samples from the grassland field also show a diamagnetic component for the deeper layers.     

M?ssbauer analysis of high-energy mechanical-milled sand fraction of a magnetic soil developing on basalt

A sample of the coarse sand fraction from the soil material of the A-horizon (0?C0.2 m from the soil surface) of a dusky red magnetic Oxisol was submitted to high-energy mechanical milling for different times. This assay aimed mainly at (a) monitoring the individualization of strongly aggregated mineral particles, and (b) measuring the effect of the milling pressure on the mineralogy changes of the material. These data are also intended to experimentally subside any physical model describing the mechanical behavior of the superficial soil layer that is subjected to intensive machine management, in agriculture fields. Powder X-ray data reveal that some mineralogical phases, notably gibbsite, disappear soon after the first few hours milling. The 298 K-transmission Mössbauer spectrum for the non-milled sand sample shows a qualitatively typical pattern for the sand fraction of basalt derived soils, with magnetically ordered sextets, assignable mainly to hematite and maghemite, and an intense central (super)paramagnetic Fe^3?+? doublet. For the milled samples, spectra revealed progressive spectral reduction of the magnetic hyperfine structure, with concomitant increase of relative subspectral areas due to (super)paramagnetic phases, as the milling time increased. This result is consistent with the reduction of measured saturation magnetization, from 4.96(8) J T^???1 kg^???1, for the non-milled sample, to 3.26(7) J T^???1 kg^???1, for the sample milled for 8 hours.     

Chemical and mineralogical analyses of a weathering mantle developing on peridotite of the mining area for nickel in Cerro Matoso, Colombia

Four samples were collected at several depths in a weathering mantle developing on peridotite, found in a mining area for nickel of Cerro Matoso, about 20 km southwest of Monte Libano, Department of Córdoba, Colombia. Samples represent the main stratigraphy of the mantle. Powder X-ray diffractometry, RT Mössbauer spectroscopy, saturation magnetization measurements and conventional chemical analysis on the whole and chemically treated samples, and on some of their magnetic extracts, were used to give some details of the main occurring mineralogical phases in the mantle, particular of the magnetic iron oxides.     

Die Oele

Ohne ZusammenfassungRom 1891 und 1893.Publicazione del Laboratorio Chimico Centrale delle Gabelle.Nach dem italienischen Original für die Zeitschrift für analytische Chemie. bearbeitet von Dr. D. Holde.Bei dem Umfang der vorliegenden Monographie war eine Besprechung derselben im Bericht über die Fortschritte der analytischen Chemie nicht möglich. Um daher die wichtige Arbeit unseren Lesern zugänglich zu machen, veröffentlichen wir die vorliegende selbstständige Bearbeitung des Herrn Dr. D. Holde an dieser Stelle der Zeitschrift.     

Stereoconvergent Generation of a Contrasteric syn‐Bicyclopropylidene (=syn‐Cyclopropylidenecyclopropane) by Stille‐Like Coupling

Stereoisomerically pure endo‐ and exo‐7‐halo‐7‐(trimethylstannyl)benzonorcar‐3‐enes (=endo‐ and exo‐(1‐halo‐1a,2,7,7a‐tetrahydro‐1H‐cyclopropa[b]naphthalen‐1‐yl)trimethylstannane) 4 and 6 were selectively obtained by lithium? tin or magnesium? tin transmetalation in good yields (Scheme 2 and 3). The reaction of these compounds with copper(I) thiophene‐2‐carboxylate (CuTC) produced in both cases the corresponding C_S‐symmetric bicyclopropylidene (=cyclopropylidenecyclopropane) syn‐ 1 , a single diastereoisomer (Schemes 5 and 6). The structure of syn‐ 1 was undoubtedly elucidated by X‐ray single crystal diffraction. The coupling mechanism of the carbenoid cyclopropane is discussed (Scheme 7).