Abstract This article explores the performance of foil thrust bearings under misalignment conditions, highlighting the need for a fully coupled simulation model to capture their thermo-mechanical behavior. The in-depth multiphysical nonlinear finite element model used here calculates foil and rotor disk deformations and temperatures as well as the film pressure and temperature. Misalignment causes each bearing pad to have unique height functions, pressure loads, and power losses, making single-pad analysis insufficient. The proposed model consists of a rotor with a multipad air foil thrust bearing, accurately representing misaligned configurations. Frequently, performance maps are used to show the relationship between thrust load and power loss of the thrust bearing. The main finding of this work lies in the proof of the existence of two characteristic performance limit curves for air foil thrust bearings, which limit the possible performance area. Bearing operation without misalignment marks the limit curve with the lowest losses, while the other limit curve is generated at increasing misalignment angles while maintaining the lowest allowable gap height to avoid mixed lubrication conditions. The here presented two limit curves may be of high practical interest since they define the operation boundaries of the thrust bearing and describe possible operation points for arbitrary misalignment configurations. For the case without misalignment, classical 1D performance lines are sufficient. However, if misalignment is considered, the bearing performance has to be described by 2D performance areas.

Structured Appetite Assessment in Children with Chronic Kidney Disease.

In high-precision optical systems such as laser optics, astronomical observation, and semiconductor lithography, anti-reflection coatings are crucial for light transmittance, imaging quality, and stability, but traditional designs face modeling challenges in balancing ultralow reflectivity, high wavefront quality, and manufacturability amid multi-dimensional parameter coupling and multi-objective constraints. This study addresses these by proposing a unified mathematical modeling framework integrating a Symmetric five-layer high-low refractive index alternating structure (V-H-V-H-V) with dual-scale nanostructures, employing a constrained quasi-Newton optimization algorithm (L-BFGS-B) to minimize reflectivity, wavefront root-mean-square (RMS) error, and surface roughness root-mean-square (RMS) in a six-dimensional parameter space. The Sellmeier equation is adopted to calculate wavelength-dependent material refractive indices, the model uses the transfer matrix method for the Symmetric five-layer high-low refractive index alternating structure’s reflectivity, incorporates nano-surface height function gradient correction, sub-wavelength modulation, and radial optimization, applies Zernike polynomials for low-order aberration correction, quantifies surface roughness via curvature proxies, and optimizes via a weighted objective function prioritizing low reflectivity. Numerical results show the spatial average reflectivity at 632.8 nm reduced to 0.13%, the weighted average reflectivity across five representative wavelengths in the 550–720 nm range to 0.037%, the reflectivity uniformity to 10.7%, the post-correction wavefront RMS to 11.6 milliwavelengths, and the surface height standard deviation to 7.7 nm. This framework enhances design accuracy and efficiency, suits UV nanoimprinting and electron beam evaporation, and offers significant value for high-power lasers, lithography, and space-borne radars.

Background:Oculomotor nerve palsy caused by craniocerebral injury often leads to a significant decline in patients’ quality of life. This study aims to explore a comprehensive treatment approach combining Uyghur medicine, rehabilitation training, and acupuncture therapy, and to present a case report evaluating its clinical efficacy in improving ocular motor function and related symptoms.Case presentation:A patient sustained craniocerebral injury due to a traffic accident and presented with severe oculomotor nerve palsy. Initial head CT scan revealed multiple intracranial injuries.Interventions:The patient received comprehensive treatment consisting of Uyghur medicine guided by differential diagnosis, acupuncture therapy, and structured ocular motor rehabilitation training. The rehabilitation training was administered by a certified rehabilitation therapist with an intermediate professional title and included: eye movement exercises (10–15 times/day), eyelid lifting training (10–20 times/day), visual rehabilitation training (10–15 times/day), and pupillary response training (2–3 times/day), all conducted over a 20-day period. Clinical outcomes, including palpebral fissure height, diplopia score, and pupillary function, were systematically evaluated by the rehabilitation therapist at admission, on day 10, on day 24 (pre-discharge). The overall quality of life of patients was assessed using the 36-item Short Form Health Survey. The study was approved by the institutional ethics committee, and written informed consent was obtained from the patient.Results:Following comprehensive treatment, the patient demonstrated sustained improvement. The 10-day assessment revealed complete resolution of left ptosis and exotropia. Only mild diplopia persisted during esophoria, with moderate improvement in pupillary asymmetry (approximately 1 mm difference). The pre-discharge assessment at 24 days confirmed complete resolution of all primary symptoms (including ptosis, strabismus, and diplopia; diplopia score: 0). Pupil size, shape, and light reflexes returned to normal. No symptom recurrence was observed at the 3-month follow-up; CT imaging demonstrated complete hematoma absorption, fracture healing, and bone remodeling. The patient’s 36-item Short Form Health Survey quality of life assessment showed significant improvement across all dimensions.Conclusion:This case demonstrates that an integrated treatment approach combining Uyghur medicine, rehabilitation training, and acupuncture yields significant therapeutic efficacy in improving ocular motor dysfunction secondary to complex traumatic brain injury.

This paper introduces an iceberg-based digital risk twin (DRT) framework for the health monitoring of complex engineering systems. The proposed model transforms multidimensional sensor and contextual data into a structured, interpretable three-dimensional geometry that captures both observable and latent risk components. Each monitored parameter is represented as a vertical geometric sheet whose height encodes a normalized risk level, producing an evolving iceberg structure in which the visible and submerged regions distinguish emergent anomalies from latent degradation. A formal mathematical formulation is developed, defining the mappings from the risk vector to geometric height functions, spatial layout, and surface composition. The resulting parametric representation provides both analytical tractability and intuitive visualization. A case study involving an aircraft fuel system demonstrates the capacity of the DRT to reveal dominant risk drivers, parameter asymmetries, and temporal trends not easily observable in traditional time-series analysis. The model is shown to integrate naturally into AI-enabled health management pipelines, providing an interpretable intermediary layer between raw data streams and advanced diagnostic or predictive algorithms. Owing to its modular structure and domain-agnostic formulation, the DRT approach is applicable beyond aviation, including power grids, rail systems, and industrial equipment monitoring. The results indicate that the iceberg representation offers a promising foundation for enhancing explainability, situational awareness, and decision support in the monitoring of complex engineering systems.

ABSTRACT We present an improved height function technique aimed at obtaining smooth curvature in three dimensions. The new approach is designed for estimating curvature from the volume of fluid (VOF) field. Motivated by the volume‐preserved mean curvature (VPMC) motion, an iterative procedure is implemented to eliminate oscillations from the curvature field while simultaneously ensuring consistency with the VOF field. To validate the new method, the curvature of 2D and 3D drops is considered. Numerical tests demonstrate the efficient elimination of high‐frequency errors in the local curvature, and the total volume enclosed by the interface is preserved. Considering the equilibrium of the static droplet problem, the spurious current is also effectively suppressed. The proposed method is further extended to an adaptive mesh and validated through the free oscillation of a 2D droplet. Finally, the accuracy and efficiency of the improved height function technique applied to 3D problems are confirmed through the simulation of a liquid droplet impact onto a deep liquid pool.

In the present article, we define a notion of good height functions on quasi-projective varieties V defined over number fields and prove an equidistribution theorem of small points for such height functions. Those good height functions are defined as limits of height functions associated with semi-positive adelic metrization on big and nef ℚ -line bundles on projective models of V satisfying mild assumptions. Building on a recent work of the author and Vigny as well as on a classical estimate of Call and Silverman, and inspiring from recent works of Kühne and Yuan and Zhang, we deduce the equidistribution of generic sequence of preperiodic parameters for families of polarized endomorphisms with marked points.

A Lower Bound on Forcing Numbers Based on Height Functions

Background: Air pollution is a major environmental health concern in rapidly urbanizing regions of India, with growing evidence that chronic exposure adversely affects respiratory health. Adolescents are particularly vulnerable, as lung growth and maturation continue during this critical developmental period. Urban environments typically exhibit higher levels of ambient air pollution compared to rural areas, potentially leading to disparities in lung function among adolescents. Purpose: The purpose of this study was to compare lung function parameters among urban and rural adolescents in Lucknow, India, and to examine the association between environmental exposure and respiratory health outcomes. Methods: A cross-sectional comparative study was conducted among 50 school-going adolescents aged 10–16 years, including 25 participants each from urban and rural areas of Lucknow. Spirometric measurements— Forced Vital Capacity (FVC), Forced Expiratory Volume in one second (FEV₁), and the FEV₁/FVC ratio—were assessed using standardized spirometry protocols. Descriptive statistics were computed, and inferential analyses included independent samples t-tests, chi-square tests for prevalence comparison, and Pearson correlation analysis to examine associations between lung function and anthropometric variables. Results: Rural adolescents demonstrated significantly higher mean values of FVC, FEV₁, and FEV₁/FVC ratio compared to their urban counterparts (p < 0.001). The prevalence of lung function impairment (FEV₁ < 80% predicted) was substantially higher in the urban group (32%) than in the rural group (11%), with the difference being statistically significant (χ² = 12.57, p < 0.001). Strong positive correlations between height and lung function parameters were observed in both groups, confirming physiological consistency. Conclusions: The findings indicate significant urban–rural disparities in adolescent lung function, with poorer respiratory outcomes among urban adolescents. These results suggest that chronic exposure to higher levels of ambient air pollution in urban settings may impair lung growth and function. The study highlights the urgent need for targeted public health interventions, improved air quality control, and school-based respiratory health screening programs to protect adolescent lung health.

Comparative analysis of bending moduli in one-component membranes via coarse-grained molecular dynamics simulations.

Effects of Isotonic and Isometric Exercise of Lower Trapezius and Serratus Anterior on Shoulder Height and Respiratory Function in College Students with Round Shoulder Posture

We present the Primacohedron, a unified framework linking p-adic string resonances, zeta-function spectra, and emergent spacetime geometry. By extending non-Archimedean string amplitudes and constructing a spectral correspondence that maps Riemann–Dedekind zeros to a Hermitian operator, the model reproduces GUE-type fluctuations temporally and closed-string coherence spatially. A curvature–spectral duality yields emergent geometry, holographic behaviour, and dynamically Bekensteinsaturating learning. The framework further incorporates Diophantine geometry: radicals and height functions arise as spectral-energy sums of prime resonances, and the abc-inequalityemerges as a curvature-stability condition on an adelic manifold. An adelic operator pair (Hspec, Hht) encodes analytic zeros and heights simultaneously, suggesting a geometric route toward Riemann Hypothesis (RH) and abc via curvature regularity. Finally, we extend the structure using perfectoid geometry and p-adic Hodge theory. Perfectoid tilting links mixed- and equalcharacteristic layers through a curvature-preserving duality, while Hodge filtrations provide a cohomological interpretation of spectral dimensionality and arithmetic time. Together, these developments position the Primacohedron as a geometric, cohomological, and operatortheoretic paradigm for understanding analytic and Diophantine phenomena within a single adelic spacetime.

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat two-dimensional space. We first prove that any rotationally symmetric two-dimensional membrane embedded in flat three-dimensional space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric two-dimensional membrane. We use it to explicitly construct a class of transient two-dimensional manifolds with a nontrivial metric and height function but "zero average curvature," which we dub "tablecloth manifolds." The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, nonexistence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

This study investigates the use of machine learning (ML) models to improve the accuracy of organ dose prediction in whole-body Positron Emission Tomography/Computed Tomography (PET/CT) imaging using the 18F-Fluorodeoxyglucose (18F-FDG) radiotracer. Nine ML models: Gaussian Process Regression (GPR), Ensemble Methods (ENS), Stepwise Linear Regression (SLR), Efficient Linear Regression (ELR), Support Vector Machines (SVM), Efficient Linear Regression (ELR), Tree Regression (TR), Kernel Approximation Regression (KAR), and Neural Networks (NN), were evaluated and validated based on their ability to predict organ dose based on demographic parameters such as weight, height, age, and organ function. The results revealed that the best-performing model was highly dependent on the specific organ and patient gender. The optimized Gaussian Process Regression with Bayesian Optimization (GPR+BO) model showed strong performance, particularly for the male brain (R² = 0.91) and gallbladder (R² = 0.94). However, the Ensemble (ENS) model demonstrated superior or equivalent performance for other organs in male patients, including the kidneys (R² = 0.94) and lungs (R² = 0.95). For female patients, model performance also varied, with the NN+BO model showing the best predictive accuracy for the liver (R² = 0.93). Gender-based analysis indicated that female patients absorbed higher organ doses despite similar radiotracer levels, with notable differences observed in the brain (0.36 ± 0.05 mGy for females vs. 0.33 ± 0.05 mGy for males) and lungs (0.22 ± 0.03 mGy for females vs. 0.18 ± 0.03 mGy for males). These findings show the importance of adjusting radiotracer doses based on physiological variations to ensure accurate, patient-specific dose management. This study uniquely integrates GPR+BO, significantly enhancing predictive accuracy and potentially improving patient safety by enabling personalized radiation dose in clinical PET/CT procedures.

The Primacohedron provides a unifying adelic framework in which numbertheoretic, spectral, and geometric structures arise from prime-indexed resonance modes. Building on its interpretation of the non-trivial zeros of the Riemann zeta function as the spectrum of a Hilbert–Pólya–type operator, this work extends the construction to Diophantine geometry and the abc conjecture. We show that radicals and height functions naturally correspond to spectral-energy sums of prime resonances, while the abc inequality emerges as a curvature-stability condition on an underlying adelic manifold. Within this spectral–Diophantine duality, violations of RH or abc manifest as curvature singularities of a unified spectral–height geometry. We further introduce an adelic operator pair (Hspec,Hht) encoding L-function zeros and arithmetic heights simultaneously, propose a curvatureanomaly correspondence linking analytic and Diophantine pathologies, and outline a programme suggesting how a completed Primacohedron—extended to motivic L-functions and Vojta theory—could imply both RH and abc through a single geometric regularity principle. This synthesis positions the Primacohedron as a candidate framework for an arithmetic spacetime whose curvature governs both the analytic behavior of zeta and L-functions and the Diophantine behaviour of rational points, offering a geometric route toward long-standing conjectures in number theory [1-5]

Abstract Disclosure: M. Shirley Bezerra: None. B. Zemel: None. R.J. Gallop: None. R. Walega: None. S. Schwarzenberg: None. S.D. Freedman: None. G.M. Solomon: None. C.L. Chan: None. A. Kelly: None. Context: Low bone mineral density (BMD) and increased fracture risk are common in individuals with cystic fibrosis (CF). Recent advances in CF care include development of elexacaftor-tezacaftor-ivacaftor (ETI), a therapy that in a large majority of patients restores function of the aberrant CF transmembrane conductance regulator protein. The extent to which ETI may benefit BMD alongside its observed positive effects on lung function, body mass index (BMI), and inflammation was a focus of the endocrine sub-study of PROMISE, a multicenter, prospective observational study of clinically prescribed ETI (NCT04038047). Objective: To examine changes in whole-body (WB), lumbar spine (LS), and hip areal BMD (aBMD, g/cm2) in the 24-30 months (mos) following initiation of ETI therapy. Methods: Participants were aged >12 years at enrollment, had at least one F508del mutation, and were recruited from one of 16 CF Foundation Therapeutics Development Network centers designated for the PROMISE endocrine sub-study. Dual-energy X-ray absorptiometry (DXA) scans of the WB, LS, and hip, and measures of height, weight, and pulmonary function (ppFEV1) were collected before and following 12-18 mos and 24-30 mos of ETI therapy. Changes in aBMD standard deviation scores (aBMDz), calculated using pediatric and Hologic reference ranges for youth and adults, respectively, were examined using longitudinal mixed-effects models accounting for within-individual correlated measures. BMIz and ppFEV1 were included as covariates. Results: BMD of the WB, LS, and hip was low at baseline for youth (WB less head aBMDz [mean; 95%CI]: -0.94; -1.22 to -0.66; LS aBMDz: -0.34; -0.60 to -0.08; hip aBMDz: -0.48; -0.80 to -0.15) and adults (WB aBMDz: -0.36; -0.69 to -0.03; LS aBMDz: -0.60; -0.86 to -0.35; hip aBMDz: -0.44; -0.61 to -0.27) compared to age and sex-matched peers without CF. Mixed-model results for youth (n=60 at baseline; average age 15 years [range: 12-19.8]; 48% female) revealed a decrease in WB less head (β-coefficient=-0.27; 95%CI: -0.46 to -0.09, p=0.004), spine (β=-0.26; 95%CI: -0.42 to -0.10, p=0.002), and hip (β=-0.29; 95%CI: -0.45 to -0.13, p=0.001) aBMDz between baseline and 12-18 mos. These changes persisted but did not worsen at 24-30 mos. BMIz and ppFEV1 were positively associated with aBMDz in all models. Changes in adult (n=74 at baseline; average age 28 years [range: 20-58.8]; 51% female) aBMDz were also negative, but modest compared to youth (no β-coefficient > -0.11). Conclusion: Youth aBMDz was lower at multiple skeletal sites 12-18 mos after ETI initiation, and these changes persisted out to 24-30 mos. Adult aBMDz generally remained unchanged across visits. These results do not support improved BMD in people with CF on ETI therapy over 2 years. Future analyses will seek to use a historical control group to assess the extent to which ETI may slow negative trends in aBMDz and affect long-term bone fragility. Presentation: Saturday, July 12, 2025

On the duality between height functions and continuous spin models

Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries . We prove a complete classification of the regularity of minimizers and frozen boundaries for all dimer models for a natural class of polygonal domains, much studied in numerical simulations and elsewhere. In particular, we show that the frozen boundaries are always algebraic curves. Our classification also implies that the Pokrovsky‐Talapov law holds for all dimer models at a generic point on the frozen boundary and, in addition, shows a very strong local rigidity of dimer models, which can be interpreted as a geometric universality result. Indeed, we prove a converse result, showing that any geometric situation for any dimer model is, in the simply connected case, realized already by the lozenge model. To achieve these goals we develop a new study on the boundary regularity for a class of Monge–Ampère equations in non‐strictly convex domains, of independent interest, as well as a new approach to minimality for a general dimer functional. In the context of polygonal domains, we give the first general results for the existence of gas domains for minimizers.

Polygenic mutations play a significant role in the etiology of various growth-related disorders and bone deformities, influencing multiple physiological processes. Understanding the impact of polygenic mutations is crucial for the diagnosis, genetic counseling, and management of these complex conditions. A boy first evaluated at 9 years and 10 months for short stature was diagnosed with compound heterozygous mutations in PLEC, CD96, and RNU4ATAC genes, with comorbid congenital multiple epiphyseal dysplasia and growth hormone deficiency. These mutations collectively contributed to severe short stature, skeletal deformities, and delayed neurodevelopment. Orthopedic surgeries were performed at 9 years and 10 months (first intervention), 11 years and 6 months (second intervention), and 12 years and 9 months (third intervention), while growth hormone therapy (GHT) was initiated at 11 years and 10 months. Over 25 months of GHT, his height increased by 18cm, bone age advanced by five years, and gait improved. Final clinical evaluation at 13 years and 11 months confirmed sustained improvements in height (137cm) and motor function. This case involves a child with short stature caused by rare mutations of PLEC, CD96, and RNU4ATAC. This is the first case report documenting the concurrent presence of all three rare mutations. Orthopedic surgery and GHT were employed to improve the patient's development and quality of life. We propose that early identification of high-risk factors, genetic screening, and comprehensive treatment can enhance therapeutic effectiveness and improve the patient's quality of life.

Background:The foot changes shape in response to rotational motion; however, the specific nature of these changes and their relationship to hallux valgus remain unclear. In this study, we aimed to examine the relationship between foot shape alterations due to rotational motion and the hallux valgus angle.Methods:Foot shape in healthy adult participants was measured using a three-dimensional (3D) foot scanner. Differences in foot morphology due to rotational motion were analyzed using Dunnett’s multiple comparisons method. Additionally, multiple regression analysis was conducted to identify foot shape factors associated with changes in the hallux angle.Results:On the rotational side, the foot arch was higher, and the hallux angle tended toward varus. In contrast, on the non-rotational side, the arch was lower, and the hallux angle tended toward valgus. The forefoot, midfoot, and medial-lateral malleolus inclination angles showed angular patterns that opposed changes in the calcaneus inclination angle. Multiple regression analysis revealed that, on the rotational side, higher forefoot height and varus displacement of the digitus minimus were associated with a more varus displacement of the hallux angle. On the non-rotational side, a lower navicular height, valgus displacement of the digitus minimus, lower forefoot height, and an everted midfoot inclination angle were associated with a more valgus displacement of the hallux angle.Conclusion:Foot shape changes induced by rotational motion are influenced by the kinetic chain and weight-bearing position resulting from lower leg rotation. The hallux valgus angle appears to be modulated by both forefoot transverse height and medial longitudinal arch function. These findings may inform targeted interventions such as exercise therapy and custom insole design.Clinical relevance: This study suggests that insoles providing support to the forefoot transverse and medial longitudinal arches may help mitigate hallux valgus progression by reducing mechanical stress on the hallux.