A group theory approach towards some rational difference equations

A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.Comment: 19 page

Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic

Consumer bankruptcy: Decision, choice and access to credit afterwards

Data availability statement: The data that support the findings of this study are available from the UK's Office for National Statistics (ONS). Restrictions apply to the availability of these data, which were used under license for this study. Data are available from https://beta.ukdataservice.ac.uk/datacatalogue/series/series?id=2000056#!/access-data with the permission of ONS and UK Data Service.Copyright © 2023 The Authors. We examine the effects of the bankruptcy benefit and adverse events on the consumer bankruptcy decision. Employing zero-inflated ordered probit models and a unique longitudinal survey of approximately 66,000 individuals in Great Britain, we find that consumers are more likely to enter into bankruptcy proceedings when the bankruptcy benefit increases and when they become unemployed. We find that the effects of adverse events differ across bankruptcy types. Individuals who experience the onset of health problems are more likely to choose reorganization of debts (i.e., income gleaning), whereas individuals who get divorced or separated are more likely to prefer the discharge of debts (i.e., fresh start). We also examine access to credit after bankruptcy. We find that individuals are excluded from the credit markets post-bankruptcy and the impact differs across bankruptcy types. Credit exclusion for fresh starters is dramatic, swift but short-lived, while for income gleaners, it is gradual, slow but lasts longer

Pathogenic Parkinson's disease mutations across the functional domains of LRRK2 alter the autophagic/lysosomal response to starvation

LRRK2 is one of the most important genetic contributors to Parkinson's disease (PD). Point mutations in this gene cause an autosomal dominant form of PD, but to date no cellular phenotype has been consistently linked with mutations in each of the functional domains (ROC, COR and Kinase) of the protein product of this gene. In this study, primary fibroblasts from individuals carrying pathogenic mutations in the three central domains of LRRK2 were assessed for alterations in the autophagy/lysosomal pathway using a combination of biochemical and cellular approaches. Mutations in all three domains resulted in alterations in markers for autophagy/lysosomal function compared to wild type cells. These data highlight the autophagy and lysosomal pathways as read outs for pathogenic LRRK2 function and as a marker for disease, and provide insight into the mechanisms linking LRRK2 function and mutations

Surgical techniques for the treatment of ankyloglossia in children: a case series

This paper reports a series of clinical cases of ankyloglossia in children, which were approached by different techniques: frenotomy and frenectomy with the use of one hemostat, two hemostats, a groove director or laser. Information on the indications, contraindications, advantages and disadvantages of the techniques was also presented. Children diagnosed with ankyloglossia were subjected to different surgical procedures. The choice of the techniques was based on the age of the patient, length of the frenulum and availability of the instruments and equipment. All the techniques presented are successful for the treatment of ankyloglossia and require a skilled professional. Laser may be considered a simple and safe alternative for children while reducing the amount of local anesthetics needed, the bleeding and the chances of infection, swelling and discomfort

Kinetic, Isotherm and Thermodynamic Analysis on Adsorption of Cr(VI) Ions from Aqueous Solutions by Synthesis and Characterization of Magnetic-Poly(divinylbenzene-vinylimidazole) Microbeads

The magnetic-poly(divinylbenzene-1-vinylimidazole) [m-poly(DVB-VIM)] microbeads (average diameter 53–212 μm) were synthesized and characterized; their use as adsorbent in removal of Cr(VI) ions from aqueous solutions was investigated. The m-poly(DVB-VIM) microbeads were prepared by copolymerizing of divinylbenzene (DVB) with 1-vinylimidazole (VIM). The m-poly(DVB-VIM) microbeads were characterized by N2 adsorption/desorption isotherms, ESR, elemental analysis, scanning electron microscope (SEM) and swelling studies. At fixed solid/solution ratio the various factors affecting adsorption of Cr(VI) ions from aqueous solutions such as pH, initial concentration, contact time and temperature were analyzed. Langmuir, Freundlich and Dubinin–Radushkvich isotherms were used as the model adsorption equilibrium data. Langmuir isotherm model was the most adequate. The pseudo-first-order, pseudo-second-order, Ritch-second-order and intraparticle diffusion models were used to describe the adsorption kinetics. The apparent activation energy was found to be 5.024 kJ mol−1, which is characteristic of a chemically controlled reaction. The experimental data fitted to pseudo-second-order kinetic. The study of temperature effect was quantified by calculating various thermodynamic parameters such as Gibbs free energy, enthalpy and entropy changes. The thermodynamic parameters obtained indicated the endothermic nature of adsorption of Cr(VI) ions. Morever, after the use in adsorption, the m-poly(DVB-VIM) microbeads with paramagnetic property were separeted via the applied magnetic force. The magnetic beads could be desorbed up to about 97% by treating with 1.0 M NaOH. These features make the m-poly(DVB-VIM) microbeads a potential candidate for support of Cr(VI) ions removal under magnetic field

Genome-Wide Analysis of Nucleotide-Level Variation in Commonly Used Saccharomyces cerevisiae Strains

Ten years have passed since the genome of Saccharomyces cerevisiae–more precisely, the S288c strain–was completely sequenced. However, experimental work in yeast is commonly performed using strains that are of unknown genetic relationship to S288c. Here, we characterized the nucleotide-level similarity between S288c and seven commonly used lab strains (A364A, W303, FL100, CEN.PK, ∑1278b, SK1 and BY4716) using 25mer oligonucleotide microarrays that provide complete and redundant coverage of the ∼12 Mb Saccharomyces cerevisiae genome. Using these data, we assessed the frequency and distribution of nucleotide variation in comparison to the sequenced reference genome. These data allow us to infer the relationships between experimentally important strains of yeast and provide insight for experimental designs that are sensitive to sequence variation. We propose a rational approach for near complete sequencing of strains related to the reference using these data and directed re-sequencing. These data and new visualization tools are accessible online in a new resource: the Yeast SNPs Browser (YSB; http://gbrowse.princeton.edu/cgi-bin/gbrowse/yeast_strains_snps) that is available to all researchers