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We investigate the properties of matrices that emerge from the application of Fourier series to Jacobi matrices. Specifically, we focus on functions defined by the coefficients of a Fourier series expressed in orthogonal polynomials. In the operational formulation of integro-differential problems, these infinite matrices play a fundamental role. We have derived precise calculation formulas for their elements, enabling exact computation of these operational matrices. Numerical results illustrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Terrestrial supergene goethites of known ages record information on changes in weathering conditions through time. Here we present a database of (U-Th)/He ages and U and Th contents of goethites from different weathering environments around the globe. By consolidating published data collected at four different laboratories and unpublished data collected at the Noble Gas Laboratory at Caltech, we aim to give an overview of the work carried out by geochronologists and geochemists in the last 20 years. The database contains 2597 (U-Th)/He ages of goethites from 10 countries; most of the ages come from Brazil and Australia. [ABSTRACT FROM AUTHOR]

Increases in temperature and pressure caused by rapid burial of sediments seaward of the Sumatra subduction zone have been hypothesized to trigger dehydration reactions that diagenetically strengthen sediments and contribute to the formation of an over‐pressured pre‐décollement, which together facilitate the occurrence of large shallow earthquakes. We present paleomagnetic, rock magnetic, and electron microscopic analyses from drill cores collected offshore Sumatra at Site U1480 during IODP Expedition 362 that support this hypothesis. The older pre‐fan units (Late Cretaceous to early Paleocene) were deposited when Site U1480 was moving rapidly northward with the Indian plate from a paleolatitude of 50° to 30°S, which would equate to expected absolute paleomagnetic inclinations of 70°–43°. Most of the older pre‐fan sediments, however, have shallow observed inclinations (shallower than ±20°), indicating that the sediments were overprinted when Site U1480 was located near the paleoequator, as it has been since the early Oligocene. Electron microscopic observations reveal that the pre‐existing detrital magnetite grains have undergone pervasive dissolution and alteration by hydrothermal fluids. The diagenesis observed is consistent with mineral dehydration, possibly driven by rapid burial of pelagic sediments by the ∼1250 m thick Nicobar Fan sequence. In addition, the elevated burial temperature also facilitated the smectite to illite conversion reaction. We hypothesize that chemical reactions resulted in the formation of fine‐grained magnetite that records a chemical remanent magnetization overprint. This overprint is consistent with the alteration occurring after burial by the thick Nicobar Fan sequence sometime in the past few million years. Plain Language Summary: Sediments and rocks commonly contain magnetic minerals that record the direction and intensity of Earth's magnetic field as they are being emplaced, thus preserving an ancient record of the geomagnetic field. Subsequent alteration of the magnetic minerals caused by heating and/or fluid circulation can result in the acquisition of secondary magnetizations (i.e., remagnetization) that may overprint or completely reset the primary ancient magnetization. Such remagnetization provides evidence of the physical and chemical changes that have occurred. Here through paleomagnetic, rock magnetic, and microscopic analyses of the deeper older (pre‐fan) stratigraphic sequence cored offshore Sumatra, we find that hydrothermal fluids, resulting from mineral dehydration driven by rapid burial of this sequence by younger, thick Nicobar Fan sediments, led to pervasive secondary remagnetization. Consequently, the newly formed magnetite recorded a much younger paleomagnetic field, leaving a shallow overprint that probably occurred sometime in the past few million years. The dehydration reactions also increased the strength of the sediments entering the subduction zone and aided in the formation of slip surfaces (called décollements), possibly contributing to the shallow, large earthquakes that have generated tsunamis off Sumatra. Key Points: The 60–67 Ma pre‐fan sediments offshore Sumatra were most likely remagnetized since deposition of the Nicobar Fan sediments, which began at ∼9 MaRemagnetization of pre‐fan sediments caused by mineral dehydration may be linked to shallow seismogenic slip off SumatraMagnetic properties of input sediments in the subduction margin record conditions that may have facilitated the generation of earthquakes [ABSTRACT FROM AUTHOR]

Hysteresis, referring to the property of a system whereby some temporary shocks cause permanent effects, has showed to be important to explain the dynamics of aggregate employment. What is not yet addressed properly in the literature is the differentiation of hysteresis effects according to activity sectors. This subject is important in order to understand whether severe recessions, like the one that followed the COVID-19 pandemic with its recognized heterogeneous immediate effects at the sectoral level, have permanent effects, and prospectively for applying adequate stabilizing fiscal and monetary policies, and possibly other specific measures, to prevent excessive market shocks even if they are perceived to be temporary. For this purpose, we apply the play hysteresis model, which describes a dynamic process whereby non-convex adjustment costs create intervals of weak reaction of employment to forcing variables, and spurts in employment in reaction to large or cumulative small labour demand shocks. The model is implemented by means of a switching employment equation. The switching parameter is interpreted as an 'employment band of inaction' that summarizes the magnitude of the hysteretic effects. We have found significant hysteresis effects in the employment dynamics across sectors, and these are especially important for industry. [ABSTRACT FROM AUTHOR]