Stability Results Research Articles

Effects of an Instability Training Program Using Global Versus Selective Instability Devices on Dynamic Balance and Ankle Stability in Young Amateur Soccer Players

Background/Objectives: Both Sides Utilized it is one of the most employed global instability devices (GID), but it is difficult to progress and select a particular foot structure. In this sense, the Blackboard has been created as selective instability device (SID). The aim of this study is to compare the effects of both devices on balance and ankle stability. Methods: The study was designed as a randomized controlled clinical trial. Twenty healthy amateur soccer players were divided into two groups: GID and SID. Both performed balance training (4-weeks, 3 days/week). Ankle balance and stability were assessed. Paired t-tests were used to analyze the pre-, post-, and between-groups differences. Results: No differences were found between the groups. Significant intra-group changes were found in both groups for posterolateral balance and summation. Moreover, posteromedial balance increased in the GID group. No changes were found in ankle stability results. Conclusions: A balance intervention using GID or SID is effective in improving general and posterolateral balance. Moreover, the GID intervention improved posteromedial balance.

Existence and Ulam’s Stability Results for the First-Order Hahn Difference Systems

Existence and Ulam’s Stability Results for the First-Order Hahn Difference Systems

Role of Surfactants on Electrocatalytic Activity of Co/Al Layered Double Hydroxides For Hydrogen and Oxygen Generation

AbstractLayered double hydroxides (LDHs) have recently attracted much attention in the scientific community as a prominent catalyst for oxygen evolution reaction (OER) because they are economical, extremely stable, and highly active. Literature on LDH alone and their hybrids for catalyzing water oxidation are readily available, but LDH catalyzing hydrogen evolution reaction (HER) is meager. Here, we synthesized Co/Al‐based LDH systems that efficiently perform as bifunctional electrocatalysts for both HER and OER. Exfoliation of this layered material via anion intercalation into a few layers further enhanced its activity. In this work, we reported the synthesis of Co/Al LDHs via coprecipitation followed by hydrothermal method and different surfactant‐functionalized LDHs (with anionic surfactant: SDS, cationic surfactant: CTAB, and nonionic surfactant: PEG 4000). SDS‐modified LDH (s LDH) showed notable stability and competent results in hydrogen evolution in addition to oxygen evolution. The exfoliation of s LDH caused enhancement in the high specific surface area about 6.8 times compared to pristine LDH, as evident from BET data. The onset potential for HER as obtained from the polarization curve for s LDH is −0.41 V versus RHE, with Tafel slope of 67.4 mV/dec. Similarly, OER onset potential and corresponding Tafel slope are 1.53 V versus RHE at 10 mA/cm2 and 90.2 mV/dec, respectively.

Influence of the PAN:PEO Ratio on the Morphology of Needleless Electrospun Nanofiber Mats Before and After Carbonization

Nanofiber mats with a high surface-to-volume ratio can be prepared by electrospinning. The Porosity is sometimes reported to be tunable by blending different materials, e.g., water-soluble poly(ethylene oxide) (PEO) with not water-soluble poly(acrylonitrile) (PAN). Here, nanofiber mats were electrospun from different PAN:PEO ratios, using a wire-based electrospinning machine “Nanospider Lab”. Investigations of the as-spun nanofiber mats as well as of membranes after washing off the water-soluble PEO by scanning electron microscopy (SEM) revealed severe differences in the nanofiber mat morphologies, such as varying fiber diameters and especially non-fibrous areas in the carbonized nanofiber mats, depending on the amount of PEO in the nanofiber mat as well as the molecular weight of the PEO. Similarly, the ratio and molecular weight of PEO influenced the results of stabilization and carbonization. This paper discusses the possibility of tailoring nanofiber porosity for the potential use of PAN nanofiber mats in tissue engineering, filtration, and other applications.

Effect of Phycocyanin and Butylated Hydroxytoluene on the Oxidative Stability of Safflower Oil: A Comprehensive Kinetic Investigation

ABSTRACTSafflower includes both saturated and unsaturated fatty acids especially high levels of polyunsaturated fatty acid (PUFA). The addition of antioxidants during oil processing is one of the most effective methods. The aim of this research was to evaluate the oxidative stability of safflower oil supplemented with phycocyanin (PC) (200, 300, and 400 ppm), or butylated hydroxytoluene (BHT) (200 ppm), at 80, 90, and 100°C during the storage time. Oxidative stability of oil was measured through the assay of primary and secondary oxidation products: Peroxide value (PV) and thiobarbituric acid reactive substances (TBARS) were evaluated, respectively. Results showed that the addition of PC at 300 and 400 ppm caused the lowest peroxide levels. In addition, the oxidation reactions of this oil followed a first‐order kinetic model for PV and TBARS. The amounts of PV and TBARS were dependent on the storage temperature; according to the Arrhenius equation, the activation energy (Ea) of the samples that contain 300 and 400 ppm PC decreased in all the tested temperatures compared to control. Results of the oxidative stability indicated that PC may have superior antioxidant properties than BHT and can potentially inhibit the oil oxidation. The sample containing 300 ppm PC demonstrated heightened efficacy in suppressing primary oxidation. Moreover, the results of sensory evaluation test showed that the 300 ppm PC sample received the highest rating for overall quality, which confirm that 300 ppm PC sample could be the best sample to decrease the oxidative stability in safflower oil.

A globally divergence-free weak Galerkin finite element method with IMEX-SAV scheme for the Kelvin–Voigt viscoelastic fluid flow model with high Reynolds number

In this manuscript, we present a globally divergence-free weak Galerkin finite element method with the IMEX-SAV scheme for solving the Kelvin–Voigt viscoelastic fluid flow model. Firstly, the weak Galerkin finite element method is used to analyze the spatial discretization, this method can yield globally divergence-free velocity solutions. Secondly, the IMEX-SAV difference scheme is adopted in the temporal discretization for the fully discrete scheme, and we can obtain the unconditional stability result for the velocity. In addition, combined with the stabilization idea, the method can not only reduce the spurious numerical oscillation at the high Reynolds number but also yield the uniform results that the constants in the error estimates do not explicitly depend on the inverse power of the physical parameters of the Kelvin–Voigt viscoelastic fluid flow model. Finally, several numerical experiments are performed to verify the theoretical results.

Effects of Different Auditory Stimuli and Cognitive Tasks on Balance in Healthy Young Adults

Introduction: This study investigated the effect of different auditory stimuli and cognitive tasks on balance in healthy young adults. Methods: Thirty-three participants, aged 23.33 ± 2.43 years, were included in the study. The hearing levels of the participants were determined. Static and dynamic postural stability and limits of stability (LOS) tests were performed in the absence of auditory stimuli, in the presence of spondee word lists at 70 dB(A) and in the presence of spondee+white noise (−6 dB signal-to-noise ratio [SNR]), while auditory stimuli were presented bilaterally with supra-aural headphones. Participants were asked to repeat the words they listened to while performing balance-related tasks. Results: No significant differences between the three conditions were observed in the postural stability and LOS results. Increase in total repetition error was observed as the listening task became more difficult. Conclusion: The presence of auditory stimuli and the cognitive tasks did not cause any changes in the participants’ balance.

Well-posedness and exponential stability of piezoelectric beam with thermal effect and boundary or internal distributed delay

In this work, we focus on a one-dimensional initial-boundary value problem of a thermoelastic piezoelectric beam in the presence of magnetic effects with distributed delay acting in the mechanical equation. The well-posedness of the system is initially demonstrated by applying semigroup theory (Hille-Yosida theorem). Also, based on the construction of a Lyapunov functional, which is equivalent to the energy functional of the problem through multiplier techniques, we show that a unique dissipation through frictional damping is strong enough to ensure exponential stabilization of the model. Next, the results are compared to those of the electrostatic or quasi-static approaches. Moreover, we consider the fully dynamic and electrostatic or quasi-static piezoelectric beams with thermal effects, boundary feedback controllers and boundary distributed delays and using the multipliers technique, we establish an exponential stability result of the solution. Our results are related to the distributed delay weights. Finally, we give some numerical tests to illustrate the theoretical result.

Metric measure spaces with Ricci bounds from below

In this survey we introduce new results on metric measure spaces with Ricci curvature bounded below, so-called R C D \mathrm {RCD} spaces, including stability results of several energies with respect to measured Gromov-Hausdorff convergence, Weyl’s law, and a characterization of noncollapsed RCD spaces.

Effect of Graft Choice for ACL Reconstruction on Clinical Outcomes in Combined ACL and MCL Injuries: Comparison Between Bone-Patellar Tendon-Bone and Hamstring Autografts.

Background/Objectives: The optimal graft, particularly in combined anterior cruciate ligament (ACL) and medial collateral ligament (MCL) injuries, remains controversial. We evaluated the influence of graft choice between bone-patellar tendon-bone (BPTB) and hamstring autografts on clinical outcomes in combined ACL and MCL injuries. Methods: This retrospective analysis included patients with concurrent ACL and MCL injuries who underwent single-bundle ACL reconstruction with BPTB (group B) or hamstring (group H) grafts, between 2010 and 2019, with a ≥2-year follow-up. Patients were classified based on the MCL injury grade (I, II, or III). Clinical outcomes were assessed through knee stability evaluations using valgus stress radiographs and the KT-2000 arthrometer, patient-reported outcomes using the International Knee Documentation Committee (IKDC) subjective score and Lysholm score, and radiologic outcomes using the IKDC radiographic grade. Results: The study included 169 patients (group B, 92; group H, 77). No significant between-group differences in knee stability or functional outcomes were found after follow-up. Within the same MCL injury grade, particularly in high-grade MCL injuries, BPTB grafts resulted in significantly better medial stability (side-to-side difference in medial joint opening on valgus stress radiographs: grade II, p = 0.006; grade III, p = 0.039) and functional outcomes (IKDC subjective score: grade II, p = 0.045; grade III, p = 0.038) than hamstring grafts. In the hamstring group, higher-grade MCL injuries were associated with worse outcomes (Lysholm knee score, p = 0.009; IKDC subjective score, p = 0.015). Conclusions: Graft choice in ACL reconstruction with concomitant MCL injuries may affect clinical outcomes, particularly in high-grade MCL injuries. Although both graft types performed similarly overall, BPTB grafts provided superior medial stability and functional results in higher-grade MCL injuries. However, caution is needed when interpreting these results due to limitations such as the small sample size and the lack of randomization in graft selection.

Studying the Antioxidant and Antimicrobial Activity of Lipsticks Made with Phycoerythrin Under the Influence of Different Magnetic Fields

Background: Several studies have shown the benefits of magnetic treatment on the productivity of secondary metabolites, growth, and the state of microalgae cultures Objective: This study examined the antioxidant and antimicrobial activity of lipsticks made with phycoerythrin (PE) extracted from the cyanobacterium Nostoc sp. under the influence of different magnetic fields (30 mT and 60 mT). Material and Methods: After cyanobacterial culture under magnetic fields of 30 mT and 60 mT, the PE was extracted and lipsticks were formulated. The primary evaluation methods used in this study are melting point, breaking point, linoleic acid peroxidation assay, force of application, stability, surface abnormalities, skin irritation, thixotropy character, dispersibility test, perfume stability, colorimetric assay, antioxidant, and microbial analysis Results: The 30 mT treatment showed the highest concentration, purity, dry weight, antioxidant activity, and percentage of PE extraction compared to control cultures. No significant differences were found in the melting point, stability, thixotropy character, dispersibility, or perfume stability tests. The breaking point and force of application decreased significantly during 30 days. Peroxidation assay tests revealed lipstick increased oxidation and antioxidant activity after 30 days of 30 and 60 mT treatments compared to non-PE cultures. The study found that the amount of ΔE increased significantly in cultures without PE over time, while this increase was lower in magnetic field-treated cultures. However, no signs of crystal formation, surface wrinkles, liquid secretion, itching, or skin irritation were observed in 30 days of 30 and 60 mT magnetic treatments compared to control cultures with PE. Microbial analyzes over 30 days showed a significantly lower number of bacteria under magnetic fields than control cultures. In addition, the results of counting Escherichia coli and coliform bacteria were negative for thirty days. The antioxidant activity of PE was significantly higher in magnetic field-treated cultures. The number of Staphylococcus aureus decreased significantly in all cultures under magnetic field influence. Conclusions: The overall results of this study showed that magnetic fields had a significant effect in many evaluation tests on the culture of cyanobacteria Nostoc sp. As a result, lipsticks made with extracted PE have more antioxidant and antimicrobial activity

Strong Stability for a Viscoelastic Transmission Problem under a Nonlocal Boundary Control

The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui and A. Benaissa. Namely, they focused on a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with an emphasis on rough interfaces and nonlinear dynamic (possibly, nonlocal) boundary conditions along the interface, where a transmission problem in the presence of a boundary control condition of a nonlocal type was investigated in these papers. Owing to the semigroup theory, we prove the question of well-posedness. For the very rare cases, we combined between the frequency domain approach and the Borichev–Tomilov theorem to establish strong stability results.

Optical properties and energy transfer of Tm3+ single-doped and Tm3+-Tb3+ co-doped transparent glass-ceramics containing NaGd(MoO4)2 single phase

Tm3+ single-doped and Tm3+-Tb3+ co-doped SiO2–B2O3–Na2O–ZnO–MoO3-Gd2O3 glasses were successfully prepared by the melt-quenching process. X-ray diffraction and transmittance measurements were used to determine that the optimal heat treatment regime consisted of crystallization at 620 °C for 5 h and transparent glass-ceramics containing the NaGd(MoO4)2 single phase were obtained. The characterization results by SEM confirmed that the size of the crystals precipitated in the glass matrix was on the nanometer level. The effects of different contents of Tm2O3 on the luminescent properties of glass-ceramics in this system were explored. The results showed that the emission peak at 453 nm (1D2→3F4) had the highest intensity when Tm2O3 was doped with 0.5 mol% under the wavelength at 359 nm excitation. In addition, with the gradual increase of Tb2O3 contents, the luminescence colour of the Tm2O3–Tb2O3 co-doped glass-ceramics gradually shifted from blue to green. This indicates its potential application in blue-green light display technologies and various other areas. The experimental results of the water resistance stability of the samples show that the co-doped glass-ceramic still has good luminescence stability after being immersed in water, which provides further favourable support for its application.

TRANSMISSION AND CONTROL DYNAMICS OF ROTAVIRUS DIARRHEA MODEL WITH DOUBLE DOSE VACCINATION

This study introduces a six-compartmental mathematical model (S, , , E, I, R) to examine the impact of administering a double dose vaccine on the dynamic spread of diarrhea within a community. The mathematical analysis shows the existence of equilibrium points for both disease-free and endemic states in the model. The basic reproduction number was determined using the Next Generation Matrix. Analysis has shown that the basic reproduction number which indicates the disease-free equilibrium point is locally asymptotically stable. Also, using a suitable Lyapunov functional for the model system expressed in state variables and parameters defining the dynamic characteristics of spread and control strategies of the rotavirus diarrhea to obtain the global stability of disease-free equilibrium point over time. A numerical simulation was carried out by Wolfram Mathematica to show the effect of a second-dose vaccine. The inclusion of a double-dose vaccine has been found to have a significant effect on completely eliminating the outbreak of diarrhea. This is evidenced by the local and global stability results, which indicate that effective measures have been taken to prevent the reintroduction or transmission of the disease, and if there may be a risk of outbreaks or reemergence of the disease, very little continuous monitoring and intervention strategies are required to maintain control as this should be taken seriously by medical practitioners or policy health makers.

A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term

In this work, we propose a finite difference scheme for Caputo’s fractional derivative transport equation in time and space, with a zero-order term. A new error estimation of the approximate solution has been demonstrated. By introducing an approximation of the Caputo derivative, we proved that the convergence is of order 2-α in time, and 2-β in space, for 0<α;β<1. Results of conditional stability and convergence of the numerical method are discussed. Finally a numerical implementation was presented to show the conformity between the theoretical and numerical approach of the finite difference scheme.

On the stability of electrovacuum space-times in scalar–tensor gravity

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Investigation of Changes in Tooth Colour After the Use of Different Aligners.

Clear aligner treatment is an orthodontic treatment that is custom-made with 3D printers without the use of conventional metal or porcelain wires and brackets. It is a modern orthodontic method used to correct tooth positions that need to be corrected aesthetically and functionally. Aim This study aimed to compare the discolouration of teeth and clear aligners after 15 days of full-time use of clear aligners. Materials and methods The 20 patients in the study group had used clear aligners for 45 days, including three different clear aligners for 15 days. In addition, 20 patients were included as a control group to measure the difference in tooth discolouration. Retaining attachments using G-Aenial (GC Corp, Tokyo, Japan) and 3M ESPE (St. Paul, MN, USA) flowable composites were placed crosswise to each patient in the distal regions of all lateral and canine teeth. The performance of three aligner plates (Zendura Flex (Bay Materials LLC, Fremont, CA, USA); Duran (ScheuDental GmbH, Iserlohn, Germany); and Taglus (Laxmi Dental Export Pvt. Ltd, Mumbai, India)), two fluid composite attachments, and two clear aligner cleaners regarding discoloration were tested. Each aligner was used for 15 days, and then the patient was moved to the next aligner. Colour change on the aligners and the patients' teeth were assessed from the canine to the middle third and mid-plane of the canine tooth using a VITA Easyshade V spectrophotometer (Bad Säckingen, Germany). An aligner cleaner was used immediately after the patients used their clear aligners, and then the measurements of the aligner color values were completed. The 120 aligners obtained were divided into two groups. Sixty aligners were treated with Fresh Guard (Efferdent, Lynchburg, VA, USA), and the other 60 were treated with Corega (GlaxoSmithKline, London, UK) tablets and stored in a glass of water. Results The colour stability of G-Aenial Flo was higher than that of the 3M ESPE fluid composite (p=0.040 and p=0.024). Our study determined that staining occurred in all the teeth we measured as a result of using aligner. Fresh Guard aligner cleaner caused more discoloration on Zendura and Duran aligners than Corega aligner cleaner (p<0.05). Taglus plaque was found to have more discoloration than Zendura and Duran aligner (p<0.05). Conclusion In conclusion, Duran clear aligners are preferable to other clear aligners in terms of discoloration. In addition, G-Aenial Flo can be recommended as an attachment or fluid composite because of its better color stability results.

7143 Near Term Cardiometabolic Outcomes in Transgender Boys and Men in the First Year of Gender-Affirming Testosterone Therapy

Abstract Disclosure: J. Dey: None. M. Widlansky: None. S. Cabrera: None. Background: Gender affirming testosterone (T) therapy is used to masculinize transgender adolescent men (TMs), resulting in elevated T and suppressed estradiol (E2). In cis-females, hypoestrogenism reduces vaso-protective E2-mediated estrogen receptor expression, decreasing nitric oxide vasodilation and increasing susceptibility to future vascular complications. Whether T promotes similar changes in TMs remains poorly understood. Methods: A longitudinal observational study is conducted in TMs aged 12-30yrs over the 1st yr of T, with visits at baseline (BL; pre-T), 6mo, and 1yr, compared to cis-males (CMs) with endogenous T. Primary outcome is change in brachial artery flow-mediated dilation (FMD%), an in vivo measure of vascular endothelial health, after 1yr of T. To detect a significant relative change in FMD%, 60 participants are needed (40 TMs, 20 CMs). Metabolic profile is assessed by fasting lipids, glucose, and insulin. Body composition is assessed by BMI and DEXA. Differences in mean values between and within a cohort were analyzed using the unpaired two-tailed T-test assuming unequal and equal variances, respectively. Results: To date, 51 participants are enrolled; the 21 participants who fully completed the study are included here (13 TMs, 8 CMs). At BL, TMs were post-menarchal with a mean age of 15.6yrs, ht 162.6cm, and BMI z-score 0.47. At BL, 46% were on progestin-only menstrual suppression. CMs had a mean age of 18.4yrs, ht 170.7cm, and BMI z-score 0.13. Cohorts were similar for age, height, and BMI.At BL, FMD% was higher in TMs than CMs (8.2 vs 4.6, p=0.01) but not at 1yr (6.9 vs 6.2, p=0.6). FMD% did not change in TMs receiving T over 1yr (8.2 vs 6.9, p=0.3). At BL, the brachial artery resting diameter (mm) was lower in TMs than CMs (2.6 vs 3.5, p&amp;lt;0.01) and remained such at 1-yr. Resting diameter increased in TMs over 1yr of T (2.6 vs 3.1, p&amp;lt;0.01) but not in CMs. There were no differences in resting or hyperemic flow velocity, or FMD (mm) between or within groups. At BL, % lean body mass (%LBM) was lower in TMs than CMs (60 vs 72, p&amp;lt;0.01) and estimated percent visceral adiposity tissue (%VAT) was higher (26 vs 14, p&amp;lt;0.01). In TMs, %LBM increased (60 vs 66, p &amp;lt;0.01) and %VAT decreased (26 vs 21, p&amp;lt;0.01) over 1yr of T, such that TMs and CMs were similar at 1yr. At BL, TMs had lower T but similar E2 (46 vs 27 pg/mL, p=0.2) to CMs. At 1-yr, TMs and CMs had similar T (556 vs 574 ng/dL, p=0.9) and E2 (52 vs 29, p=0.1). In TMs, T did not change E2. Lipid and glycemic indices did not change over 1yr in TMs. Conclusion: Initial analyses suggest that T does not affect FMD; however, FMD% interpretation is confounded by the small number of participants, progestins at BL in TMs, and the lower resting brachial artery diameter in TMs. The stable E2 in TMs on T may explain the stable FMD%. Overall, our findings suggest T results in relative stability of vascular and metabolic function and a beneficial shift in body composition in TMs. Presentation: 6/2/2024

Preparation and evaluation the effects of retinoic acid loaded proliposomal nanofibers on microbial biofilm inhibition

The electrospinning method involves the production of different drug delivery systems using various polymers. The production of proliposomes with electrospinning provides the hybridization of two novel drug delivery systems. Retinoic acid, also known as all-trans retinoic acid (ATRA), is a common and effective drug for acne therapy. This study aimed to prepare ATRA-loaded proliposomal nanofibers and evaluate their effectiveness on microbial biofilm inhibition. Blank and ATRA-loaded proliposomal nanofiber formulations were fabricated in various polyvinylpyrrolidone, phosphatidylcholine and cholesterol ratios. TEM images verified the rapid formation of the liposomes after the hydration of nanofibers. The vesicle size, polydispersity index and zeta potential values of self-assembled liposomes were measured. The vesicle size values were found to be 321.9–363.8 nm with PDI values varying between 0.332 and 0.511 and zeta potential values of (−16.8) to (−20.5)mV. ATRA-loaded proliposomal nanofibers provided higher bioadhesion (0.25 mJ/cm2) than the commercial cream (0.07 mJ/cm2). The short-term stability results showed that the initial characteristics remained for three months at 4 °C. The proposed ATRA-loaded self-assembled proliposomal system provided antibacterial, fungistatic or fungicidal effects superior to retinoic acid itself and inhibited biofilm formation in lower concentrations. This approach can combine the stability advantage of nanofibers in the dry state with the high effectiveness of liposomes in acne treatment presenting antibacterial and anti-biofilm-forming activity against Candida albicans and Cutibacterium acnes.

On the homology of big mapping class groups

AbstractWe prove that the mapping class group of the one‐holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once‐punctured Cantor tree surface (i.e. the plane minus a Cantor set), in particular answering a recent question of Calegari and Chen. We in fact prove these results for a general class of infinite‐type surfaces called binary tree surfaces. To prove our results we use two main ingredients: one is a modification of an argument of Mather related to the notion of dissipated groups; the other is a general homological stability result for mapping class groups of infinite‐type surfaces.