An elementary proof of the beta-gamma function identity is presented by Chen and Chen [Chen, H.-C., & Chen, H. L. (2025). The beta-gamma function identity via Taylor's formula. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2025.2573176]. In this note we remark that the limiting arguments in Section 2.3 and Appendix of Chen and Chen [Chen, H.-C., & Chen, H. L. (2025). The beta-gamma function identity via Taylor's formula. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2025.2573176] can be considerably simplified. Our alternative arguments make their proof much more accessible to students in elementary single-variable calculus classes.

This prospective, observational study examined the overall effectiveness of three online training programs to attenuate mental health concerns, enhance global well-being, and promote workplace wellness. Employees and spouses at a large R1 university self-selected one or more of three interventions. Two included contemplative training and the comparison program did not, allowing us to evaluate the potential contribution of online contemplative training to well-being programming. Validated self-report measures were used to assess outcomes at baseline and 1-month and 1-year follow-up. Among 471 participants who provided baseline and follow-up data, a statistically significant time effect and small and consistent effect sizes were observed for almost all variables. The findings of this real-world study clearly show that online contemplative training programs can enhance mental health, well-being, and, to a small degree, workplace engagement among university employees.

Treatment Efficacy for Functional Voice Disorders with Dysphonia: A Network Meta-analysis.

Introduction:Radiographic markers including the crossover sign (COS), ischial spine sign (ISS), and posterior wall sign (PWS) are commonly used to assess acetabular morphology. The aim of this study was to determine the vertical tilt or horizontal rotation needed to elicit sign changes on anterior-posterior (AP) digitally reconstructed radiographs (DRRs).Methods:CT scans of the pelvis were retrospectively collected and imported into three-dimensional (3D) imaging software to create 3D AP digitally reconstructed radiographs (DRRs). Rendered pelvises were standardized to 0° of tilt and rotation and assessed for positive or negative findings of COS, ISS, and PWS. Then, the DRR was manipulated at 1° intervals (from 0° to 20° in each direction), progressively inducing pelvic tilt in the vertical axis, and the process was then repeated in the horizontal axis. The degree at which the sign changed from positive to negative or vice versa in each hip was recorded.Results:A total of 20 hips were assessed (five men, five women). On the standardized AP pelvis radiographs, positive COS, ISS, and PWS were 45%, 25%, and 75% respectively. The mean rotation required to change COS, ISS, and PWS from positive to negative or vice versa was 7.92° ± 4.25°, 5.55° ± 2.63°, and 6.37° ± 3.89°, respectively. The mean tilt required to flip COS, ISS, and PWS was 8.80° ± 5.73°, 7.73° ± 3.65°, and 9.55° ± 4.98°.Conclusion:Close consideration should be given to pelvic position when assessing positive findings of COS, ISS, and PWS because all signs were noted to flip with small degrees of rotation and tilt.

Abstract The purpose of this note is twofold. First, we give a quick proof of Ballico–Chiantini’s theorem stating that a Fano or Calabi–Yau variety of dimension at least 4 in codimension 2 is a complete intersection. Second, we improve Barth–Van de Ven’s result asserting that if the degree of a smooth projective variety of dimension n is less than approximately $$0.63 \cdot n^{1/2},$$ 0.63 · n 1 / 2 , then it is a complete intersection. We show that the degree bound can be improved to approximately $$0.79 \cdot n^{2/3}.$$ 0.79 · n 2 / 3 .

Based mainly on part I of the Star of Redemption (the Star), this paper is divided into three main parts. First of all, the first part will mention the new thinking and its circumstances. Rosenzweig criticizes both Kant (man as a moral entity) and Hegel (the notion of totality and reduction of man to spirit). Rosenzweig justifies the need for new thinking as follows: philosophy begins with “the fear of death.” Philosophy has until now endorsed man based on concepts and essences which are inevitably abstract. Thus, he calls for a radical “new thinking.” Next, three irreducible elements (God, world, and man) and the ontological analysis of personality is the content of the second part. Cohen’s infinitesimal calculus and how the three irreducible elements generate themselves out of their own particular nothings will be mentioned. Rosenzweig argues that personality, the first stage in the ontological analysis regarding man, is an inauthentic self. Thirdly, the main content of the third part is the ontological analysis of an authentic self in the second stage (character) and third stage (self). The shift from personality to character is significant. Character is non-relational because it is a self-enclosure. In addition, the writer focuses highly on the self in its entire form (“B=B”) as metaethics. Through these analyses, Rosenzweig proves that man is both finite and infinite. Furthermore, he uses the “soul” as the self that emerges at the intersubjective level. The “soul” is both beyond “personality”, “character” and even “metaethics”. And so, man is beyond metaethics and non-definitive. In conclusion, man is not only one element alongside but also in relation to God as a living subject (in part II of the Star).

Abstract For many, pregnancy is a transformational event in a woman’s life entailing several psychological and physical changes that can become catalysts for positive personal growth. Birth-related posttraumatic growth (PTG) is one way of measuring how challenging experiences related to pregnancy and birth can influence the mother’s mental states differently with the magnitude of the specific psychological and psychosocial factors contributing to birth-related PTG yet to be mapped out. Thus, this study aimed at examining and comparing several parameters that have been suggested to contribute to birth-related PTG among women. A total of 559 women ( M age = 32.2, SD = 5.9) who gave birth in Denmark completed an online survey assessing social support, perceived control, mindfulness, and posttraumatic growth (PTG) related to their latest birth. The study found that at least a small degree of birth-related PTG was experienced by 71.4% of the women ( M = 51.4, SD = 19.8). A multiple regression analysis showed that higher social support and lower age significantly predicted higher birth-related PTG amongst the women. The findings particularly emphasize the overarching importance of experiencing a strong, personal social network when women are going through this transitional time in life. Implications for optimizing women’s opportunities for growth as they transition into motherhood are being discussed alongside ways to move this research field forward in meaningful ways.

BackgroundChronic obstructive pulmonary disease (COPD) is a chronic inflammatory disease characterized by airflow limitation and exertional dyspnea, leading to reduced exercise tolerance and physical inactivity. Nasal high-flow (NHF) therapy delivers heated and humidified gas at a high flow rate through a nasal cannula, washing out anatomical dead space, providing a small degree of positive airway pressure, improving ventilation efficiency, and reducing the work of breathing. In addition, adequate humidification may enhance ciliary clearance. The AIRVO3TM (Fisher & Paykel Healthcare, Auckland, New Zealand) is a novel portable NHF device that incorporates these features and can be used during ambulation. Using AIRVO3TM during exertion may improve exercise tolerance in patients with COPD; however, its safety and effectiveness in ambulatory patients have not yet been established.MethodsThis is a single-center, early-phase, open-label, randomized, two-period crossover pilot trial conducted at Nagasaki University Hospital, designed to evaluate the acute, within-day effects of AIRVO3TM on exercise tolerance during a single visit. Twenty patients with moderate to severe COPD will perform two 6-minute walk tests (6MWT) in a randomized order: one with AIRVO3TM and one without the device. The primary outcome is the 6-minute walk distance (6MWD). Secondary outcomes include percutaneous oxygen saturation (SpO2), transcutaneous partial pressure of carbon dioxide (PtcCO2), respiratory rate, pulse rate, Borg dyspnea scale score, time to desaturation (SpO2 ≤90%), time to PtcCO2 ≥45 mmHg, time to respiratory rate ≥22/min, walking distance to the first rest, patient-reported comfort, and subjective symptoms. Safety outcomes include the incidence of SpO2 <90%, adverse events (AEs), device-related discomfort, and withdrawal or dropout. Data will be analyzed primarily using paired t-tests and mixed-effects models that are appropriate for a crossover design.DiscussionThis trial will evaluate whether a portable NHF device increases exercise tolerance and is safe during ambulation in patients with COPD who do not require long-term oxygen therapy. By using room air [finspiratory oxygen fraction (FiO2) 21%] and focusing on high flow rather than high oxygen concentration, this study will clarify the pure effects of high-flow nasal therapy on exertional capacity. If the AIRVO3TM device is shown to be effective and acceptable, it may expand the options for pulmonary rehabilitation and daily physical activity in patients with COPD. Because all assessments are performed during a single study visit, this trial specifically evaluates short-term, acute responses to AIRVO3TM rather than long-term training effects of repeated use.Trial RegistrationThe study is registered in the Japan Registry of Clinical Trials (jRCT; trial ID jRCTs072240116; registered on February 20, 2025; https://jrct.mhlw.go.jp/latest-detail/jRCTs072240116). This article describes the protocol version 1.1 (March 11, 2025).

To evaluate the responsiveness of objective, quantifiable physiological or behavioural data measures (digital biomarkers) as outcome measures for people living with hip and/or knee osteoarthritis (OA) in community or home settings. This systematic review and meta-analysis identified eligible studies from four electronic databases. Studies were required to use a digital biomarker as an outcome measure or had data collected by a portable or wearable device, usable at home, and without expert oversight (e.g., accelerometers, smartphone devices), and collected at a minimum of two time points. Two independent reviewers conducted screening and data extraction. A meta-analysis was performed using a random-effects model. Results were reported as standardized response means (SRMs) and 95% confidence intervals (CIs). Subgroup analyses were conducted based on intervention versus non-intervention groups and across different time periods (short, medium, long-term). Risk of bias was assessed using modified criteria for evidence quality. We identified 40 studies evaluating 18 digital biomarkers. Participants had a mean age of 64 (SD=4) years, with most having knee OA. The overall quality of the studies was high. Accelerometers (95%) were the most commonly used technology type. Mobility related outcomes were the most responsive digital biomarker domain. Cadence, walking speed, and step count showed moderate (SRM = 0.65, 95% CI: 0.42-0.87), small (SRM = 0.43, 95% CI: 0.15-0.70), and trivial (SRM = 0.19, 95% CI: 0.02-0.36) degrees of responsiveness, respectively. Energy expenditure demonstrated a trivial negative responsiveness (SRM = -0.16, 95% CI: -0.31 to -0.01). All digital biomarkers identified were based on land-based activities, which limits their application for monitoring non-land-based activities such as water exercises, cycling, Tai Chi, yoga or sleep. Digital biomarkers related to mobility measures, have the potential for greater uptake in OA clinical trials to assess mobility health in community and home-settings. PROSPERO ID: CRD42024600515.

Congestion and extreme events in transportation networks are emergent phenomena with significant socioeconomic implications. In this work, we study congestion and extreme event properties on nearly-planar real urban street networks drawn from four cities and compare it with that on a regular square grid. For dynamics, we employ three variants of random walk with additional realistic transport features. In all the four urban street networks and 2D square grid and with all dynamical models, phase transitions are observed from a free flow to a congested phase as a function of the birth rate of vehicles. These transitions can be modified by traffic-aware routing protocols, but congestion cannot be entirely mitigated. In street networks without any structure, we observe a weakly congested regime with coexistence of both congested and free-flow components. This regime is suppressed in street networks with a grid-type structure (such as in parts of New York city) and is entirely absent in the regular 2D grid lattice. In the free-flow regime, extreme event occurrence probability is larger for small degree nodes than for hubs. Hence, our results indicate that studying congestion and extreme event properties on synthetic lattices are relevant for real street networks.

Sexual and gender minority (SGM) individuals often suffer from a myriad of stressors within their social environments due to stigma and its outcomes (Meyer, 2003). Conversely, social support may impact SGM individuals' psychological resilience. To quantify the impact of their interpersonal environments, the current preregistered meta-analysis included 253 studies (N=111,188) that reported associations between social support (i.e., family, peer, partner, school, work) and internalizing psychopathology (i.e., depression, anxiety, nonsuicidal self-injury, suicidality) among SGM samples. Overall, a small, negative association was observed, r=-0.26, with low levels of variance between studies. Larger effects were observed for depression than other measures of psychopathology, r=-0.29, while smaller effects were observed for suicidality, r=-0.17. Smaller effects were observed for samples with a larger share of bisexual individuals, and when a SGM-specific measure was used. Larger effects were observed for European studies performed in areas of greater structural stigma (but not for American studies). The negative association between social support and psychopathology was consistent across an array of demographic factors (e.g., age, gender, % white) and SGM identities (e.g., % gender minority). No evidence of publication bias was observed. These findings suggests that all forms of SGM social support are similarly associated with lower internalizing psychopathology to a small degree, most of all with regards to depression.

Abstract The out-of-equilibrium character of active systems is often twofold, arising from both the activity itself and from non-reciprocal couplings between constituents. A well-established measure to quantify the system's distance from equilibrium is the informatic entropy production rate. Here, we ask the question whether and how the informatic entropy production rate reflects collective behaviors and transitions in an active mixture with non-reciprocal polar couplings. &amp;#xD;In such systems, non-reciprocal orientational couplings can induce chiral motion of particles. At the field-theoretical level, transitions to these time-dependent chiral states are marked by so-called critical exceptional points. We show that at a particle level, the entropy production rate within the chiral states increases with the degree of non-reciprocity, provided it is sufficiently strong. Moreover, even at small degrees of non-reciprocity, the transitions via exceptional points leave clear signatures in the entropy production rate, which exhibits pronounced peaks at coupling strengths corresponding to the field-theoretical exceptional points. Overall, the increase and peaks of the entropy production rate mirror the susceptibility of the polarization vector at the particle level. This correspondence is supported by a field-theoretical analysis, which reveals that, in the long-wavelength limit, the entropy production rate scales with the susceptibilities of the polarization fields.

Extraction of useful work from the chaotic environments remains a captivating challenge. A gear in the bath of self-propelling eccentric particles is investigated by computer simulation. We find that the asymmetrical gear can rotate in a specific direction, with the angular speed first increasing and then decreasing as the eccentricity increases. Besides, a machine-learning model is trained to predict the angular speeds and the optimal one. Additionally, we observe that the directional rotation of a symmetric gear depends on the particle-area fraction, the persistence length of motion, and the eccentricity. Eccentricity is not conducive to the rotation of a symmetric gear, but a small degree of eccentricity can help increase the angular speed of the gear. There exist two mechanisms working for gear rotation at low eccentricity of particles: edge alignment with corner trapping and biased trapping with positive feedback. These insights suggest the tunable particle-level parameter, eccentricity, offers a promising strategy to regulate and optimize gear rotation.

Uveitis refers to inflammation of the uvea (the iris, ciliary body and choroid) but in clinical practice it encompasses intraocular inflammation affecting adjacent structures such as the retina, vitreous and optic nerve. Although it represents a relatively small proportion of ophthalmic disease overall, it is responsible for a disproportionate amount of visual morbidity, accounting for around 10% of blindness worldwide. Uveitis can be acute or chronic, infectious or immune-mediated, and may occur in isolation or in association with a systemic condition. Because the eye is exquisitely sensitive to inflammation, even small degrees of intraocular disturbance can result in substantial symptoms or complications; for this reason, timely recognition and management are of great importance.

Blunt force trauma to the larynx can cause significant damage, resulting in displaced laryngeal cartilage fractures. Vertical misalignment of the left or right vocal fold (VF) in the inferior-superior direction and scarring of the VF tissue are common outcomes. The influence of inferior-superior VF displacement and VF scarring on phonation was investigated using synthetic, self-oscillating VF models in a physiologically-representative facility. Acoustic, kinematic, and aerodynamic parameters were assessed as a function of inferior-superior vertical displacement and asymmetric VF stiffness. The combination of vertical misalignment and asymmetric VF tissue stiffness became most prominent when the inferior-superior misalignment of the VFs exceeded the thickness of the medial surface. Only a small degree of stiffness asymmetry was tolerated before VF kinematics and acoustics were significantly degraded. The position of the scarred VF relative to the healthy one also influenced outcomes. If the stiffer VF was positioned inferior to the normal VF, phonatory outcomes were poorer than when it was positioned superior to the normal VF. Measures of shimmer and jitter were more than twice as high, while cepstral peak prominence was 3-5 dB lower.

By using the geometric and algebraic properties of Bernstein polynomials, a composite method for solving the initial value problems (IVP's) with first-order, singular and nonlinear ordinary differential equations (ODE's) has been developed. The Newton’s method is incorporated into the method to solve the resulting system of nonlinear equations. The algorithm of the problem solving is reduced to the calculation of the unknown Bernstein coefficients of the approximate solution. The effectiveness of the proposed method is verified by comparing the present numerical results by other existing ones. The proposed method reduces the computation cost and gives a better approximation to the exact solution even for small degrees of approximation. Another advantage of the present method is the ability to calculate the approximate solution at each point of the solution interval in addition to the grid points.

Mitral annular disjunction (MAD) is a structural abnormality of the mitral valve increasingly detected with advanced cardiac imaging, particularly cardiac magnetic resonance (CMR). However, the clinical impact of different degrees of disjunction and the lack of standardized measurement criteria remain controversial. This study aimed to describe a series of patients with MAD assessed by CMR and to discuss, in the context of current literature, potential cut-off values that may distinguish physiological from pathological MAD. We retrospectively identified all CMR examinations performed at our institution over a 6-month period in which MAD was visible in at least two cine steady-state free precession (SSFP) projections. For each patient, we recorded MAD extent, presence of mitral valve prolapse/regurgitation, late gadolinium enhancement (LGE) pattern, and main clinical presentation. Nine patients (mean age 57 years; 5 men) were included. Larger MAD distances (&gt;4 mm) were frequently associated with non-ischemic LGE in the basal lateral wall and with valvular abnormalities, whereas smaller disjunctions (≤3 mm) were often observed in patients without significant structural disease. Non-ischemic LGE was present in 6/9 patients, all with MAD &gt; 5 mm. These observations, together with published data, support the hypothesis that small degrees of MAD may represent a frequent anatomical variant, while more extensive disjunction, especially when associated with fibrosis, may indicate a pathological substrate for arrhythmias. Standardized CMR-based criteria and validated MAD cut-off values are needed to improve risk stratification and to incorporate MAD assessment into routine clinical practice.

Following the collapse of the Avar Khaganate in the early 9th century, Transdanubia first fell under the authority of the Frankish Empire, then in less than a century later the early Magyars conquered the territory. Mosaburg/Zalavár, founded near Kis-Balaton under Frankish rule, was a highly significant regional power centre during both the Carolingian Period and in a large part of the Árpádian Age. Objectives were (1) to discover by analysing craniometric data how the rapid and radical changes in power, and the birth and history of Mosaburg centre affected the population history and structure in the Zalavár microregion between the Late Avar and Árpádian Age; (2) to provide a general anthropological profile of the 9th and 11th century inhabitants of the former power centre by examining the skeletal material of the Hadrianus Templom site, the largest local cemetery of the studied era. The Carolingian and the 11th century population of the centre was Caucasoid based on their morphoscopic traits, but around 10% of the skulls in both periods also showed some traits typical for Mongoloids. The average stature in both groups markedly exceeded the contemporaneous mean of the Carpathian Basin. The demographic and skeletal trauma data of the 11th century community indicates that they had a peaceful way of life. In contrast with this, the 9th century males had a less favourable mortality rate than females as early as in the young adult age group, and many of them had weapon injuries, including perimortem ones. This suggests that soldiers were buried in the cemetery, too, and several of them died in battle(s) fought near Mosaburg against the early Magyars before the end of the Frankish rule. The 9th and 11th century sample of the power centre share very similar craniometric features, thus most of their biological distance-based close analogies overlap. This cranial morphological complex was characteristic mainly in the western half of the Carpathian Basin, where, though presumably with a changing spatial distribution pattern over time, it was already present in the late Roman Period. Close parallels from outside the Carpathian Basin can be found in the ~9th–11th century Moravian and Vienna Basin, and in the Pontic steppe between the Late Sarmatian Period and the 13th century. The geographical roots (ancestors) of the series representing this cranial morphological complex in the Carpathian Basin may point to the Eastern-European steppe region. The local population in the Mosaburg microregion showed significant biological continuity during the studied period. Postmarital residence in the Late Avar local social system was most probably patrilocal. Most of the inhabitants of the Carolingian Period Mosaburg and its surrounding villages arrived probably from within the region to the newly founded power centre. During the 10th century the appearance of new immigrants can be detected on the territory. However, they could not change the anthropological character of the local community. The common people of the Árpádian Age Zalavár centre possibly originated mainly from those nearby “indigenous” groups of the region that had been affected only temporarily and/or to a small degree by the migration events of the Carolingian Period and the 10th century.

In this study, we examine how variations in local pressure anisotropy affect the internal structure and equilibrium of white dwarfs. A generalized anisotropy model is developed, defined by three parameters: the amplitude coefficient α₀ and the shape exponents l and k. This formulation ensures that the anisotropic pressure continuously vanishes at both the center and surface of the star while reaching a single peak in the intermediate region. By applying appropriate boundary and regularity conditions, the model allows us to determine physically stable parameter domains consistent with realistic stellar configurations. Our analysis shows that even a small degree of anisotropy can have a measurable effect on the mass–radius relation and overall compactness of white dwarfs, which may help explain the origin of super-Chandrasekhar systems observed in astrophysical data. This modeling approach provides a clear and flexible way to describe compact stars with anisotropic pressures and can also be applied to neutron and quark stars. Keywords: compact stars, white dwarfs, anisotropic pressure, stability analysis, generalized anisotropic factor

Abstract Kimberlites are the deepest derived magmas on Earth, and together with the mantle xenoliths and xenocrysts they carry, provide an unprecedented look into the composition and evolution of the mantle from the Archaean to Cenozoic. Although superficially similar to kimberlites, olivine lamproites of the Kaapvaal Craton, previously known as Group II kimberlites, are highly micaceous and represent a distinct magmatic episode to kimberlites. Both kimberlites and olivine lamproites are derived by small degrees of partial melting in the upper convective asthenospheric mantle, which then traverse the non-convective, sub-continental lithospheric mantle (SCLM) en route to Earth’s surface. The major element compositions of the parent magmas are modified during complex melt-SCLM interactions, and this leads to significant diversification of the magmas. During their ascent, they also entrain diamonds, and consequently, kimberlites and olivine lamproites form primary volcanic ore deposits on emplacement near the surface. These volcanic pipes, ~3 km in depth and several hundred metres in diameter, formed from predominantly juvenile volatile-driven eruptions. In most cases across the Kaapvaal Craton, kimberlite pipes have been significantly eroded post-emplacement and the diamonds within them have been transported toward the west coast, forming secondary alluvial diamond deposits along the way. Diamond exploration and evaluation relies on kimberlite indicator minerals, e.g., garnet, ilmenite, and clinopyroxene, which are mantle xenocrysts from the SCLM transported to the surface in kimberlite and olivine lamproite magmas. The composition of these minerals is controlled by the pressure-temperature (P-T) conditions at which they last equilibrated. The majority of diamonds form at relatively low temperatures (900 to 1200°C) but high pressures (4 to 7 GPa). These conditions are met in the SCLM and this region is termed the ‘diamond window’. A smaller proportion of diamonds have a sub-lithospheric origin likely forming in the mantle transition zone (MTZ). Thermobarometry is the approach used to constrain the P-T conditions of indicator minerals based on their chemistry. This provides a means to map the composition and thermal state of the SCLM to depths of ~200 km, and to assess the extent of a possible diamond window sampled by individual kimberlites. Ultimately, kimberlites and olivine lamproites, along with their mantle cargo, are invaluable in our understanding of the deep Earth and are economically valuable as diamond deposits.