On a functional equation for Dido's problem

By some geometrical considerations we formulate a functional equation which is related to the ancient isoperimetric problem of Dido. The continuous solution of this Dido functional equation depends on an arbitrary function. However, we show that in a class of functions of suitable asymptotic behavior at infinity, the Dido functional equation has a one-parameter family of "principal" solutions. Some applications are given

On some extensions of the Gołąb-Schinzel functional equation

Composite functional equations (arising in applications) are presented that may be interpreted as extensions of the Goląb-Schinzel equation and as modifications of d'Alembert's equation. Depending on the type of the considered equation, continuous, and finite rate of growth solutions are discussed. Geometric interpretations are given

Louse-borne relapsing fever—a systematic review and analysis of the literature: part 2— mortality, Jarisch–Herxheimer reaction, impact on pregnancy

Louse-borne relapsing fever (LBRF) is a classical epidemic disease, which in the past was associated with war, famine, poverty, forced migration, and crowding under poor hygienic conditions around the world. The disease’s causative pathogen, the spirochete bacterium Borrelia recurrentis, is confined to humans and transmitted by a single vector, the human body louse Pediculus humanus corporis. Since the disease was at its peak before the days of modern medicine, many of its aspects have never been formally studied and to date remain incompletely understood. In order to shed light on some of these aspects, we have systematically reviewed the accessible literature on LBRF since the recognition of its mode of transmission in 1907, and summarized the existing data on mortality, Jarisch–Herxheimer reaction (JHR), and impact on pregnancy. Publications were identified by using a predefined search strategy of electronic databases and a subsequent review of the reference lists of the obtained publications. All publications reporting patients with a confirmed diagnosis of LBRF published in English, French, German, and Spanish since 1907 were included. Data extraction followed a predefined protocol and included a grading system to judge the certainty of the diagnosis of reported cases. The high mortality rates often found in literature are confined to extreme scenarios. The case fatality rate (CFR) of untreated cases is on average significantly lower than frequently assumed. In recent years, a rise in the overall CFRs is documented, for which reasons remain unknown. Lacking standardized criteria, a clear diagnostic threshold defining antibiotic treatment-induced JHR does not exist. This explains the wide range of occurrence rates found in literature. Pre-antibiotic era data suggest the existence of a JHR-like reaction also in cases treated with arsenicals and even in untreated cases. LBRF-related adverse outcomes are observed in 3 out of 4 pregnancies

Tick borne relapsing fever - a systematic review and analysis of the literature

Tick borne relapsing fever (TBRF) is a zoonosis caused by various Borrelia species transmitted to humans by both soft-bodied and (more recently recognized) hard-bodied ticks. In recent years, molecular diagnostic techniques have allowed to extend our knowledge on the global epidemiological picture of this neglected disease. Nevertheless, due to the patchy occurrence of the disease and the lack of large clinical studies, the knowledge on several clinical aspects of the disease remains limited. In order to shed light on some of these aspects, we have systematically reviewed the literature on TBRF and summarized the existing data on epidemiology and clinical aspects of the disease. Publications were identified by using a predefined search strategy on electronic databases and a subsequent review of the reference lists of the obtained publications. All publications reporting patients with a confirmed diagnosis of TBRF published in English, French, Italian, German, and Hungarian were included. Maps showing the epidemiogeographic mosaic of the different TBRF Borrelia species were compiled and data on clinical aspects of TBRF were analysed. The epidemiogeographic mosaic of TBRF is complex and still continues to evolve. Ticks harbouring TBRF Borrelia have been reported worldwide, with the exception of Antarctica and Australia. Although only molecular diagnostic methods allow for species identification, microscopy remains the diagnostic gold standard in most clinical settings. The most suggestive symptom in TBRF is the eponymous relapsing fever (present in 100% of the cases). Thrombocytopenia is the most suggestive laboratory finding in TBRF. Neurological complications are frequent in TBRF. Treatment is with beta-lactams, tetracyclines or macrolids. The risk of Jarisch-Herxheimer reaction (JHR) appears to be lower in TBRF (19.3%) compared to louse-borne relapsing fever (LBRF) (55.8%). The overall case fatality rate of TBRF (6.5%) and LBRF (4-10.2%) appears to not differ. Unlike LBRF, where perinatal fatalities are primarily attributable to abortion, TBRF-related perinatal fatalities appear to primarily affect newborns

Envelopes of special class of one-parameter families of curves

In our recent paper [6] concernig some relations between the logarithmic and arithmetic means we have obtained a family of solutions a of a relevant one-parameter system of functional equations which are of the form 4>a{x) = g{^ ) + $(0, where a > 0 is the parameter, and g is a particular solution of the functional equation corresponding to the parameter a = 1. Since g completely describes the one-parameter family of solutions [0)01 > 0 , we call g to be its generator (Fragment tekstu)

Understanding Selectivity of Mesoporous Silica-Grafted Diglycolamide-Type Ligands in the Solid-Phase Extraction of Rare Earths

Rare earth elements (REEs) and their compounds are essential for rapidly developing modern technologies. These materials are especially critical in the area of green/sustainable energy; however, only very high-purity fractions are appropriate for these applications. Yet, achieving efficient REE separation and purification in an economically and environmentally effective way remains a challenge. Moreover, current extraction technologies often generate large amounts of undesirable wastes. In that perspective, the development of selective, reusable, and extremely efficient sorbents is needed. Among numerous ligands used in the liquid-liquid extraction (LLE) process, the diglycolamide-based (DGA) ligands play a leading role. Although these ligands display notable extraction performance in the liquid phase, their extractive chemistry is not widely studied when such ligands are tethered to a solid support. A detailed understanding of the relationship between chemical structure and function (i.e., extraction selectivity) at the molecular level is still missing although it is a key factor for the development of advanced sorbents with tailored selectivity. Herein, a series of functionalized mesoporous silica (KIT-6) solid phases were investigated as sorbents for the selective extraction of REEs. To better understand the extraction behavior of these sorbents, different spectroscopic techniques (solid-state NMR, X-ray photoelectron spectroscopy, XPS, and Fourier transform infrared spectroscopy, FT-IR) were implemented. The obtained spectroscopic results provide useful insights into the chemical environment and reactivity of the chelating ligand anchored on the KIT-6 support. Furthermore, it can be suggested that depending on the extracted metal and/or structure of the ligand and its attachment to KIT-6, different functional groups (i.e., C= O, N-H, or silanols) act as the main adsorption centers and preferentially capture targeted elements, which in turn may be associated with the different selectivity of the synthesized sorbents. Thus, by determining how metals interact with different supports, we aim to better understand the solid-phase extraction process of hybrid (organo)silica sorbents and design better extraction materials

Propranolol Blocks Cardiac and Neuronal Voltage-Gated Sodium Channels

Propranolol is a widely used, non-selective β-adrenergic receptor antagonist with proven efficacy in treating cardiovascular disorders and in the prevention of migraine headaches. At plasma concentrations exceeding those required for β-adrenergic receptor inhibition, propranolol also exhibits anti-arrhythmic (“membrane stabilizing”) effects that are not fully explained by β-blockade. Previous in vitro studies suggested that propranolol may have local anesthetic effects. We directly tested the effects of propranolol on heterologously expressed recombinant human cardiac (NaV1.5) and brain (NaV1.1, NaV1.2, NaV1.3) sodium channels using whole-cell patch-clamp recording. We found that block was not stereospecific as we observed approximately equal IC50 values for tonic and use-dependent block by R-(+) and S-(−) propranolol (tonic block: R: 21.4 μM vs S: 23.6 μM; use-dependent block: R: 2.7 μM vs S: 2.6 μM). Metoprolol and nadolol did not block NaV1.5 indicating that sodium channel block is not a class effect of β-blockers. The biophysical effects of R-(+)-propranolol on NaV1.5 and NaV1.1 resembled that of the prototypical local anesthetic lidocaine including the requirement for a critical phenylalanine residue (F1760 in NaV1.5) in the domain 4 S6 segment. Finally, we observed that brain sodium channels exhibited less sensitivity to R-(+)-propranolol than NaV1.5 channels. Our findings establish sodium channels as targets for propranolol and may help explain some beneficial effects of the drug in treating cardiac arrhythmias, and may explain certain adverse central nervous system effects

Surgical and functional outcome after resection of 64 petroclival meningiomas

Objective: The management of petroclival meningiomas (PCMs) remains notoriously difficult due to their close association with neurovascular structures and their complex anatomy, hence the surgical paradigm change from radical to functional resection in the past. With this study, we aimed to analyze surgical and functional outcomes of a modern consecutive series of patients with PCMs. Methods: We reviewed patient charts and imaging data of 64 consecutive patients from 2006 to 2018 with a PCM resected at our institution and compared surgical and functional outcomes between subgroups stratified by surgical approach. Results: Females comprised 67.2% of patients (n = 43), with a mean age of 55 years (median 56; range 21–84). Follow-up data were available for 68.8% and reached a mean of 42.3 months (range 1–129) with a median of 28.5 months. The mean tumor diameter was 37.3 mm (standard deviation (SD) 15.4; median 37.0). Infiltration of the cavernous sinus was observed in 34 cases (53.1%), and the lesions affected the brain stem in 28 cases (43.8%). Preoperative cranial nerve palsy was observed in 73.4% of cases; trigeminal neuropathy (42.2%), hearing loss (32.8%), and impairment of vision (18.8%) were the most common. A retrosigmoid approach was employed in 47 cases (78.1%), pterional in 10 (15.6%), combined petrosal in 2 (3.1%), and transnasal and subtemporal in 1 (1.6%). Fifteen cases (23.4%) were resected in a two-staged fashion. Gross total resection (GTR) was attempted in 30 (46.9%) cases without cavernous sinus infiltration and was achieved in 21 (70.0%) of these cases. Surgical complications occurred in 13 cases (20.3%), most commonly meningitis (n = 4; 6.3%). Postoperatively, 56 patients (87.5%) developed new cranial nerve palsy, of which 36 (63.6%) had improved or resolved on last follow up. Achieving GTR was not significantly associated with higher rates of surgical complications (chi-square; p = 0.288) or postoperative cranial nerve palsy (chi-square; p = 0.842). Of all cases, 20 (31.3%) underwent postoperative radiation. Tumor progression was observed in 10 patients (15.9%) after a mean 102 months (median 124). Conclusions: Surgical resection remains the mainstay of treatment for PCMs, with perioperative cranial neuropathies exhibiting favorable recovery rates. Most essentially, the preselection of patients with hallmarks of brain stem affection and cavernous sinus infiltration should dictate whether to strive for a functionally oriented strategy in favor of radical resection