On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Aromaticity in cyanuric acid

This study analyzes the aromatic nature of cyanuric acid (hexahydrotriazine) and some of its derivatives, in terms of aromatic stabilization energy (ASE) and electronic behavior. The simplest molecule (C3N3O3H3) is the most aromatic item out of the entire set, but some of the others also display aromatic character. The structure of all the rings is analyzed considering their molecular orbitals as well as studying the inductive effect

Efficacy and safety of preoperative preparation with Lugol''s iodine solution in euthyroid patients with Graves’ disease (LIGRADIS Trial): Study protocol for a multicenter randomized trial

Background: Currently, both the American Thyroid Association and the European Thyroid Association recommend preoperative preparation with Lugol''s Solution (LS) for patients undergoing thyroidectomy for Graves’ Disease (GD), but their recommendations are based on low-quality evidence. The LIGRADIS trial aims to provide evidence either to support or refute the systematic use of LS in euthyroid patients undergoing thyroidectomy for GD. Methods: A multicenter randomized controlled trial will be performed. Patients =18 years of age, diagnosed with GD, treated with antithyroid drugs, euthyroid and proposed for total thyroidectomy will be eligible for inclusion. Exclusion criteria will be prior thyroid or parathyroid surgery, hyperparathyroidism that requires associated parathyroidectomy, thyroid cancer that requires adding a lymph node dissection, iodine allergy, consumption of lithium or amiodarone, medically unfit patients (ASA-IV), breastfeeding women, preoperative vocal cord palsy and planned endoscopic, video-assisted or remote access surgery. Between January 2020 and January 2022, 270 patients will be randomized for either receiving or not preoperative preparation with LS. Researchers will be blinded to treatment assignment. The primary outcome will be the rate of postoperative complications: hypoparathyroidism, recurrent laryngeal nerve injury, hematoma, surgical site infection or death. Secondary outcomes will be intraoperative events (Thyroidectomy Difficulty Scale score, blood loss, recurrent laryngeal nerve neuromonitoring signal loss), operative time, postoperative length of stay, hospital readmissions, permanent complications and adverse events associated to LS. Conclusions: There is no conclusive evidence supporting the benefits of preoperative treatment with LS in this setting. This trial aims to provide new insights into future Clinical Practice Guidelines recommendations. Trial registration: ClinicalTrials.gov identifier: NCT03980132. © 202

Redox-active and DNA-binding coordination complexes of clotrimazole

DNA interactions of anticancer mononuclear Cu2+, Co2+, Zn2+, and Ni2+ complexes with the biologically active ligand clotrimazole (clotri) are reported. To fully characterize DNA binding modes for these complexes of the formulae [M(clotri)2Cl2]·nH2O (1–4), [M(clotri)2Br2]·nH2O (5,6), [M(clotri)3NO3]NO3·nH2O (9), and [M(clotri)3(NO3)2] (10), circular dichroism (CD) and linear dichroism (LD) spectroscopy, UV melting experiments, atomic force microscopy (AFM) and ethidium bromide (EtBr) displacement methods were used. Results indicate mixed electrostatic interactions, possibly through groove binding, that result in accretion and coiling of DNA. Electrochemical studies indicate that the Cu2+ complex 9 readily reduces to the reactive-oxygen-species-generating Cu+, which oxidatively damages DNA. There is a subtle correlation between log P values, calculated electrostatic potentials, and cytotoxicity of the complexes. The extent of cell-nucleus DNA-metal adduct formation in the HeLa cervix-uterine carcinoma cell line does not necessarily correlate with cytotoxicity, indicating that the nature of DNA lesions may be crucial to activity

Water in the terrestrial planet-forming zone of the PDS 70 disk

Terrestrial and sub-Neptune planets are expected to form in the inner ($<10~$AU) regions of protoplanetary disks. Water plays a key role in their formation, although it is yet unclear whether water molecules are formed in-situ or transported from the outer disk. So far Spitzer Space Telescope observations have only provided water luminosity upper limits for dust-depleted inner disks, similar to PDS 70, the first system with direct confirmation of protoplanet presence. Here we report JWST observations of PDS 70, a benchmark target to search for water in a disk hosting a large ($\sim54~$AU) planet-carved gap separating an inner and outer disk. Our findings show water in the inner disk of PDS 70. This implies that potential terrestrial planets forming therein have access to a water reservoir. The column densities of water vapour suggest in-situ formation via a reaction sequence involving O, H$_2$, and/or OH, and survival through water self-shielding. This is also supported by the presence of CO$_2$ emission, another molecule sensitive to UV photodissociation. Dust shielding, and replenishment of both gas and small dust from the outer disk, may also play a role in sustaining the water reservoir. Our observations also reveal a strong variability of the mid-infrared spectral energy distribution, pointing to a change of inner disk geometry.Comment: To appear in Nature on 24 July 2023. 21 pages, 10 figures; includes extended data. Part of the JWST MINDS Guaranteed Time Observations program's science enabling products. Spectra downloadable on Zenodo at https://zenodo.org/record/799102

MINDS. Abundant water and varying C/O across the disk of Sz 98 as seen by JWST/MIRI

MIRI/MRS on board the JWST allows us to probe the inner regions of protoplanetary disks. Here we examine the disk around the classical T Tauri star Sz 98, which has an unusually large dust disk in the millimetre with a compact core. We focus on the H$_2$O emission through both its ro-vibrational and pure rotational emission. Furthermore, we compare our chemical findings with those obtained for the outer disk from Atacama Large Millimeter/submillimeter Array (ALMA) observations. In order to model the molecular features in the spectrum, the continuum was subtracted and LTE slab models were fitted. The spectrum was divided into different wavelength regions corresponding to H$_2$O lines of different excitation conditions, and the slab model fits were performed individually per region. We confidently detect CO, H$_2$O, OH, CO$_2$, and HCN in the emitting layers. The isotopologue H$^{18}_2$O is not detected. Additionally, no other organics, including C$_2$H$_2$, are detected. This indicates that the C/O ratio could be substantially below unity, in contrast with the outer disk. The H$_2$O emission traces a large radial disk surface region, as evidenced by the gradually changing excitation temperatures and emitting radii. The OH and CO$_2$ emission are relatively weak. It is likely that H$_2$O is not significantly photodissociated; either due to self-shielding against the stellar irradiation, or UV-shielding from small dust particles. The relative emitting strength of the different identified molecular features point towards UV-shielding of H$_2$O in the inner disk of Sz 98, with a thin layer of OH on top. The majority of the organic molecules are either hidden below the dust continuum, or not present. In general, the inferred composition points to a sub-solar C/O ratio (<0.5) in the inner disk, in contrast with the larger than unity C/O ratio in the gas in the outer disk found with ALMA.Comment: Submitted to A&A on May 25 2023. 18 pages, 11 figure