In this paper we use the Mellin convolution theorem, which is related to Perron's formula. Also we introduce new explicit formulae for arithmetic function which generalize the explicit formulae of Weil for other arithmetic functions different from the Von-Mangoldt function.

We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a particular class of double-well harmonic oscillators that had been conveniently chosen for the application of the latter approach. The RRVM eigenvalues converge smoothly from above providing much more accurate results with less computational effort. Present results show that the unproved SSQMGS upper bounds do not hold.

Given the high number of vehicle-crash victims, it has been established as a priority to reduce this figure in the transportation sector. For this reason, many of the recent researches are focused on including control systems in existing vehicles, to improve their stability, comfort and handling. These systems need to know in every moment the behavior of the vehicle (state variables), among others, when the different maneuvers are performed, to actuate by means of the systems in the vehicle (brakes, steering, suspension) and, in this way, to achieve a good behavior. The main problem arises from the lack of ability to directly capture several required dynamic vehicle variables, such as roll angle, from low-cost sensors. Previous studies demonstrate that low-cost sensors can provide data in real-time with the required precision and reliability. Even more, other research works indicate that neural networks are efficient mechanisms to estimate roll angle. Nevertheless, it is necessary to assess that the fusion of data coming from low-cost devices and estimations provided by neural networks can fulfill the reliability and appropriateness requirements for using these technologies to improve overall safety in production vehicles. Because of the increasing of computing power, the reduction of consumption and electric devices size, along with the high variety of communication technologies and networking protocols using Internet have yield to Internet of Things (IoT) development. In order to address this issue, this study has two main goals: 1) Determine the appropriateness and performance of neural networks embedded in low-cost sensors kits to estimate roll angle required to evaluate rollover risk situations. 2) Compare the low-cost control unit devices (Intel Edison and Raspberry Pi 3 Model B), to provide the roll angle estimation with this artificial neural network-based approach. To fulfil these objectives an experimental environment has been set up composed of a van with two set of low-cost kits, one including a Raspberry Pi 3 Model B, low cost Inertial Measurement Unit (BNO055 - 37€) and GPS (Mtk3339 - 53€) and the other having an Intel Edison System on Chip linked to a SparkFun 9 Degrees of Freedom module. This experimental environment will be tested in different maneuvers for comparison purposes. Neural networks embedded in low-cost sensor kits provide roll angle estimations very approximated to real values. Even more, Intel Edison and Raspberry Pi 3 Model B have enough computing capabilities to successfully run roll angle estimation based on neural networks to determine rollover risks situation fulfilling real-time operation restrictions stated for this problem.

Dupilumab is used to treat atopic dermatitis patients who have proven to be refractory to previous treatments. The aim of this study was to assess evolution and patient reported outcome measures in adult patients with moderate-to-severe atopic dermatitis treated with Dupilumab in routine clinical practice. The outcomes were evaluated and registered at baseline and weeks-16, 40 and 52. The variables evaluated were: diseases severity, pruritus, stressful life events, difficulty to sleep, anxiety and depression, quality of life, satisfaction, adherence to the treatment, efficacy and safety. Eleven patients were recruited between Nov 14th 2017 and Jan 16th 2018. Demographic variables: 90% Caucasian, 82% women. Clinical variables: Mean duration of AD =17.7 (±12.8), 91% had severe disease severity. At baseline, SCORAD mean score = 61.7 (±15.5); itch was reported by 100% of patients; itch Visual Analogue Scale mean range of 8 (6-10); HADS mean total score =13.9 (±5.5); DLQI mean score =13.3 (±8.3): EQ-5D-3L mean range = 57 (30-99). At week-52 there is a significant reduction of SCORAD scores, HADS total score and improved quality of life. ¡This study confirms that Dupilumab, used for 52-weeks under routine clinical practice, maintains the improved atopic dermatitis signs and symptoms obtained at week-16, with a good safety profile.

Hydrothermal pyrite is an important source of thallium (Tl) but this rare element can be also detected in the secondary iron goethite-lepidocrocite and jarosite ores, associated to hydrothermal kerogen, manganese oxides, accessorial potassium minerals and tiny Tl-bearing clusters shielded in quartz masses. We studied Tl-bearing samples collected from Fe-Mn ores hosted in dolostone rocks sited along ca. 15 km of fossil thermal springs following a geological fault in the Lodares surroundings. Samples were analyzed by environmental scanning electron microscopy and energy dispersive spectroscopy (ESEM-EDS), electron probe micro-analysis (EPMA), inductively coupled plasma-mass spectroscopy (ICP-MS), X-ray diffraction analysis (XRD), Tl LIII-edge X-ray absorption near-edge structure (XANES) spectroscopy, Micro-Raman and Fourier transform infrared spectroscopy (FTIR). We found epithermal pyrite, sphalerite, galena and baryte and secondary gypsum, jarosite, scorodite, anglesite, goethite, epsomite and elemental sulfur produced by both hydroxylation and bacterial processes. The highest Tl contents were found in hydrothermal pyrite (200 mg kg-1), kerogen (13 mg kg-1), manganese ores (27 mg kg-1) and iron sulfate-hydroxides (142 mg kg-1). The aquatic kerogen was formed in a marine environment and later heavily carbonized during the hydrothermal processes. The Lodares outcrops exhibit interesting details on the geochemical cycle of Tl in a genetic frame of epithermal formation of pyrite and kerogen.