Smooth Curve Research Articles

Components of the Hilbert scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components

Components of the Hilbert scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components

MODEL OF RANDOM-LIKE PLANAR TRAJECTORIES WITH INTERSECTIONS

Background. Recently the task of detecting and identifying trajectories of objects whose genuine purposes are uncertain or strike threatening has become extremely important. The known approaches produce insufficiently smooth trajectories. Objective. The purpose of the paper is to build a model of generating random-like planar trajectories, which would have sufficiently smooth curves. A trajectory may have self-intersections and may intersect other trajectories. Methods. Preliminarily two starting points on a plane are generated. The distance and angle between these points are calculated, which then are successively updated to calculate new trajectory points using the polar coordinate system. A trajectory of points is generated using values of normally distributed random variables with zero mean and unit variance and four values of -uniformly distributed random variables. Results. The random-like trajectory generator has the same time complexity as its predecessors, including the direction randomization generator and its modifications. Exemplary trajectories appear very realistic. Self-intersections are important to manoeuvre and confuse the opponent side. The trajectory has four parameters to adjust its heading, scattering of points, and intensity of turns and twists. These parameters serve as magnitudes to amplify the respective properties. The highest influence has the angle-scattering parameter. Four simple conditions can be embedded to fit the trajectory within a rectangular domain. Conclusions. The suggested model should serve either for generating trajectory datasets to train manoeuvring-object detectors on them or for masking reconnaissance. The model allows balancing the trajectory smoothness and randomness.

Constructing Approximations to Bivariate Piecewise-Smooth Functions

This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve.

Association between waist circumference and lung function in American middle-aged and older adults: findings from NHANES 2007–2012

PurposeThere is a major epidemic of obesity, and many obese patients suffer from respiratory symptoms and disease. However, limited research explores the associations between abdominal obesity and lung function indices, yielding mixed results. This study aims to analyze the association between waist circumference (WC), an easily measurable marker of abdominal obesity, and lung function parameters in middle-aged and older adults using the National Health and Nutrition Examination Survey (NHANES).MethodsThis study utilized data obtained from the National Health and Nutrition Examination Survey (NHANES) spanning 2007 to 2012, with a total sample size of 6089 individuals. A weighted multiple regression analysis was conducted to assess the relationship between WC and three pulmonary function parameters. Additionally, a weighted generalized additive model and smooth curve fitting were applied to capture any potential nonlinear relationship within this association.ResultsAfter considering all confounding variables, it was observed that for each unit increase in WC, in males, Forced Vital Capacity (FVC) increased by 23.687 ml, Forced Expiratory Volume in one second (FEV1) increased by 12.029 ml, and the FEV1/FVC ratio decreased by 0.140%. In females, an increase in waist circumference by one unit resulted in an FVC increase of 6.583 ml and an FEV1 increase of 4.453 ml. In the overall population, each unit increase in waist circumference led to a FVC increase of 12.014 ml, an FEV1 increase of 6.557 ml, and a decrease in the FEV1/FVC ratio by 0.076%. By constructing a smooth curve, we identified a positive correlation between waist circumference and FVC and FEV1. Conversely, there was a negative correlation between waist circumference and the FEV1/FVC ratio.ConclusionsOur findings indicate that in the fully adjusted model, waist circumference, independent of BMI, positively correlates with FVC and FEV1 while exhibiting a negative correlation with FEV1/FVC among middle-aged and older adults in the United States. These results underscore the importance of considering abdominal obesity as a potential factor influencing lung function in American middle-aged and older adults.

Abnormal circadian rhythm of heart rate variability and their association with symptoms in patients with major depressive disorder

BackgroundHeart rate variability (HRV) is often reduced in patients with major depressive disorder (MDD) and is linked to symptoms. However, prior studies have mainly focused on short-term HRV, with limited exploration of the 24-h HRV circadian rhythm, despite its ability to comprehensively capture overall HRV distribution and dynamic fluctuations. In this study, we investigated the circadian rhythms of 24-h HRV indices in patients with MDD and their associations with symptom severity. MethodsWe recorded 24-h electrocardiograms in 73 patients with MDD (53 in major depressive episode and 20 in remission period) and 31 healthy controls. An extended cosine model was used to model the circadian rhythm of six HRV indices by five parameters: the mesor, amplitude, duty cycle, curve smoothness, and acrophase. Symptom severity was evaluated using the Hamilton Depression Scale and Hamilton Anxiety Scale. ResultsCompared with the control group, patients with MDD had a significantly smaller SampEn mesor, higher HF duty cycle, and lower heart rate (HR) duty cycle. They also had a significantly higher curve smoothness for HR, RMSSD, and HF. The mesor for SampEn, along with the curve smoothness for HR and ln RMSSD, were associated with certain symptoms in patients with MDD.Limitations.The cross-sectional design and psychiatric treatment of most patients with MDD limited our findings. ConclusionPatients with MDD exhibit abnormal HRV circadian rhythms that are associated with symptoms. Moreover, 24-h ECG monitoring may potentially serve as an adjunct value to objectively evaluate clinical symptoms in these patients.

The association between ferritin levels and all-cause mortality in stroke patients.

The purpose of study was to describe the association between ferritin and all-cause mortality of cases with stroke. Clinical data derived from Multiparameter Intelligent Monitoring in Intensive Care were analyzed. The primary endpoint was 30-day mortality. The potential prognostic roles of Ferritin L were analyzed by Cox proportional hazard models. The independent prognostic roles of Ferritin L in the cases were analyzed by smooth curve fitting. Concerning 30-day mortality, the HR (95% CI) for a high Ferritin (≥373) was 1.925 (1.298, 2.854; p = 0.00113), compared to a low ferritin (< 373). After adjusting for multiple confounders, the HR (95% CI) for a high Ferritin (≥373) was 1.782 (1.126, 2.820; p = 0.01367), compared to a low Ferritin (< 373). A non-linear association between Ferritin and 30-day mortality was found. Using recursive algorithm and two-piecewise linear regression model, inflection point (IP) was calculated, which was 2,204. On the left side of the IP, there was a positive relationship between Ferritin and 30-day mortality, and the effect size, 95% CI and p value were 1.0006 (1.0004, 1.0009) p < 0.0001, respectively. On the right of the IP, the effect size, 95% CI and p value were 1.0000 (1.0000, 1.0000) and 0.3107, respectively. Ferritin was associated with increased risk of stroke; it is important to further examine the association if the increased uric acid would increase the outcome of stroke in a longitudinal study. The non-linear relationship between Ferritin and all-cause mortality of stroke was observed. Ferritin was a risk factor for the outcome of stroke when ferritin was <2204.

The spectrum of Grothendieck monoid: Classifying Serre subcategories and reconstruction theorem

The Grothendieck monoid of an exact category is a monoid version of the Grothendieck group. We use it to classify Serre subcategories of an exact category and to reconstruct the topology of a noetherian scheme. We first construct bijections between (i) the set of Serre subcategories of an exact category, (ii) the set of faces of its Grothendieck monoid, and (iii) the monoid spectrum of its Grothendieck monoid. By using (ii), we classify Serre subcategories of exact categories related to a finite dimensional algebra and a smooth projective curve. For this, we determine the Grothendieck monoid of the category of coherent sheaves on a smooth projective curve. By using (iii), we introduce a topology on the set of Serre subcategories. As a consequence, we recover the topology of a noetherian scheme from the Grothendieck monoid.

Effective cone of the blowup of the symmetric product of a curve

Let C C be a smooth curve of genus g ≥ 1 g \geq 1 and let C ( 2 ) C^{(2)} be its second symmetric product. In this note we prove that if C C is very general, then the blowup of C ( 2 ) C^{(2)} at a very general point has nonpolyhedral pseudo-effective cone. The strategy is to consider first the case of hyperelliptic curves and then to show that having polyhedral pseudo-effective cone is a closed property for families of surfaces.

Association between weight-adjusted waist index and testosterone deficiency in adult American men: findings from the national health and nutrition examination survey 2013–2016

BackgroundTestosterone deficiency (TD) and obesity are globally recognized health concerns, with a bidirectional causal relationship between them. And a newly discovered obesity indicator, the Weight-Adjusted-Waist Index (WWI), has been proposed, demonstrating superior adiposity identification capability compared to traditional body mass index (BMI) and waist circumference (WC) indicators. Therefore, we present the inaugural investigation into the associations of WWI with total testosterone levels and the risk of TD.MethodsData restricted to the National Health and Nutrition Examination Survey (NHANES) between 2013 and 2016 were analyzed. Only males aged > 20 years who completed body measures and underwent serum sex hormone testing were potentially eligible for analysis. Weighted multivariable linear regression and logistic regression analyses were employed to investigate the relationships between WWI and total testosterone levels, and the risk of TD, respectively. Smooth curve fittings and weighted generalized additive model (GAM) regression were conducted to examine the linear relationship among them. Additionally, subgroup analyses with interaction tests were performed to assess the stability of the results.ResultsFinally, a total of 4099 participants with complete data on testosterone and WWI were included in the formal analysis. The mean age of study participants was 46.74 ± 0.35 years with a TD prevalence of 25.54%. After adjusting all potential confounders, the continuous WWI displayed a negative linear relationship with total testosterone levels (β=-61.41, 95%CI: -72.53, -50.29, P < 0.0001) and a positive linear relationship with risk of TD (OR = 1.88, 95%CI: 1.47, 2.39, P < 0.0001). When WWI was transformed into quartiles as a categorical variable, participants in Q4 exhibited lower total testosterone levels (β=-115.4, 95%CI: -142.34, -88.45, P < 0.0001) and a higher risk of TD (OR = 3.38, 95% CI: 2.10, 5.44, P < 0.001). These associations remained stable in subgroup analyses without significant interaction (all P for interaction > 0.05).ConclusionsThis investigation firstly unveiled a negative linear association between WWI and total testosterone levels, coupled with a positive linear relationship with the prevalence of TD in U.S. male adults aged 20 years and older. Further studies are needed to validate the potential utility of WWI for the early identification and timely intervention of TD.

Association between life's essential 8 and male biochemical androgen deficiency: evidence from NHANES 2013-2016.

To evaluate the association of Life's Essential 8 (LE8) and its subscales with male biochemical androgen deficiency (MBAD) and total testosterone based on the data from the national health and nutrition examination survey (NHANES) database. Data of males aged 20 years or older from NHANES of 2013-2016 were extracted. LE8 score was calculated based on American Heart Association definitions. Total testosterone (TT) values were measured in NHANES using precise isotope dilution liquid chromatography. MBAD was defined as serum TT of <300 ng/dL. Univariate and multivariable analyses were conducted. Propensity score matching (PSM) and weighted regression after matching were added as sensitivity analyses. The generalized additive model, smooth curve fitting, and the recursive algorithm were used to determine the potential inflection points. Piecewise regression models with log-likelihood ratio test were used to quantify nonlinear effects. A total of 3094 participants who were males and aged 20 years or above were included. Out of them, 805 males were diagnosed with MBAD. After adjusting the confounders in the multivariable model, LE8 was independently associated with MBAD (OR 0.96, P < 0.001) and TT (β 2.7, P < 0.001). The association remained robust even after PSM. The non-linear relationship of LE8 behaviors score with MBAD and TT was revealed. LE8 was an independent protective factor of MBAD and a feasible approach to promote male endocrine sexual function.

Unraveling microstructural evolution in air-entrained mortar and paste: Insights from MIP and micro-CT tomography amid cyclic freezing-thawing damage

Understanding the microstructure evolution during the cyclic freezing-thawing process is crucial to studying the deterioration mechanisms of concrete under cyclic freezing-thawing. In this study, air voids were entrained into cement mortar and paste by AEA and polymeric microspheres. Mercury intrusion porosimetry (MIP) and micro-CT techniques were integrated to investigate the microstructure of the specimens with various freezing-thawing cycles. After subjecting the Ref. and AEA mixed mortar to 100 and 200 freezing-thaw cycles, an increase in porosity and pore entrapment was observed from the MIP results, suggesting the occurrence of damage induced by cyclic freezing-thawing. Conversely, in the microspheres mixed mortar, the presence of surface adsorbed moisture led to an initial increase in porosity and pore entrapment after 100 freezing-thaw cycles, followed by a decrease after 200 cycles, indicating a healing effect. Micro-CT analysis revealed that while the AEA mixed specimens exhibited higher air content than the microspheres mixed specimens, the latter showed a greater number of voids, which ultimately enhanced their resistance to freezing-thawing. The micro-CT results unveiled that air bubbles tended to merge in AEA mixed specimens, adversely affecting their resistance to freezing-thawing. Conversely, the microsphere-incorporated specimens displayed smooth void distribution curves, indicating a well-distributed air void system that enhances their freezing-thawing resistance. This work suggests that microspheres can be a great candidate for air-entraining materials. Combining the MIP and micro-CT analysis can better understand the microstructure change of concrete with cyclic freezing-thawing.

Relationship between preoperative hemoglobin levels and length of stay in elderly patients with hip fractures: A retrospective cohort study.

Globally, hip fractures in elderly individuals are a prevalent and serious issue. Patients typically have a longer length of stay (LOS), which increases the risk of complications and increases hospitalization costs. Hemoglobin (Hb) is a routine blood test that is associated with disease prognosis. This study aimed to investigate the relationship between preoperative Hb and LOS in elderly hip fracture patients and to determine a reliable transfusion threshold. The clinical data of hip fracture patients (aged ≥ 60 years) admitted to the Department of Orthopaedics, Shenzhen Second People's Hospital, between January 2012 and December 2021 were retrospectively analyzed. Multiple linear regression analysis was used to assess the linear relationship between preoperative Hb and LOS. Smooth curve fitting was performed to investigate potential nonlinear relationships. In the case of discovering nonlinear relationships, a weighted two-piecewise linear regression model was built, and the inflection points were determined using a recursive algorithm. Subgroup analyses were conducted based on age and gender. A total of 1444 patients with an average age of (77.54 ± 8.73) years were enrolled. After adjusting for covariates, a nonlinear relationship was found between preoperative Hb and LOS. The two-piecewise linear regression model revealed an inflection point of 10 g/dL. On the left of the inflection point (Hb < 10 g/dL), the LOS was reduced by 0.735 days for every 1 g/dL increase in Hb (β = -0.735, 95% confidence interval: -1.346 to -0.124, P = .019). On the right side of the inflection point (Hb > 10 g/dL), the relationship was not statistically significant (β = 0.001, 95% confidence interval: -0.293 to 0.296, P = .992). In elderly hip fracture patients, there is a nonlinear association between preoperative Hb and LOS. However, when Hb levels were <10 g/dL, there was a negative correlation with the LOS. No correlation was observed when Hb levels were >10 g/dL. These findings underscore the importance of timely intervention to manage Hb levels in elderly patients with hip fractures, potentially reducing hospitalization durations and associated complications.

Association between visceral adiposity index and infertility in reproductive-aged women in the United States

Over the years, obesity has become more commonplace and has had a substantial impact on several medical specialties, including reproductive medicine. The potential correlation between the visceral adiposity index (VAI) and infertility has yet to be determined. Women between the ages of 18 and 45 were included in this cross-sectional study, which was conducted as part of the National Health and Nutrition Examination Survey (NHANES) between 2015 and 2020. Three tertiles were used to group VAI levels. Subgroup analysis and weighted binary logistic regression were employed to investigate the independent relationship between VAI and infertility. Smooth curve fitting was used to explore nonlinear relationships. This cross-sectional study followed the criteria of the STROBE guidelines. Of the 1231 participants, 127 were infertile women aged 18–45 years. A higher VAI was associated with a higher prevalence of infertility (OR = 1.22, 95% CI:1.03–1.45), which remained consistent across all subgroups (p > 0.05 for all interactions). We demonstrated a positive nonlinear association between VAI and infertility using a smooth curve fit. A higher visceral adiposity index level is positively correlated with a higher incidence of infertility among women in the United States. Women who are infertile can be identified using the visceral obesity index, and controlling visceral obesity may help lower the chances of becoming infertile.

Gender differences in the association between dietary protein intake and constipation: findings from NHANES.

Dietary factors play a crucial role in the development and management of chronic constipation, yet the relationship between dietary protein intake and constipation remains underexplored. This study aims to investigate the association between dietary protein intake and the prevalence of constipation among American adults, with a focus on potential gender differences, using large-scale national data. Data from 14,048 participants aged 20 and above (7,072 men and 6,976 women) from the National Health and Nutrition Examination Survey (NHANES) 2005-2010 were analyzed. The Bristol Stool Form Scale's types 1 (separate hard lumps, resembling nuts) and 2 (sausage-shaped, but lumpy) were used to define constipation. A 24-h dietary recall technique was used to measure dietary protein intake. After controlling for covariates, the association between protein consumption and constipation risk was examined using multivariable logistic regression, smooth curve fitting, and testing for gender interaction effects. We then further determined the threshold effect between dietary protein intake and constipation risk. Constipation was present in 7.49% of people overall, with a higher proportion among women (10.19%) than among males (4.82%). In men, higher protein intake was significantly associated with a lower rate of constipation. However, in women, higher protein intake correlated with an increased risk of constipation, and the interaction between gender was significant (P for interaction = 0.0298). These results were corroborated by smooth curve fits, which also demonstrated a dose-response effect. Further threshold effect analysis showed that the turning points of dietary protein intake differed between male and female participants (119.42 gm/day for men; 40.79 gm/day for women). The association between dietary protein intake and constipation was different in different genders with threshold effect. For men, moderately increasing protein intake could be beneficial, while for women, exceeding a certain level may increase the risk of constipation. These insights are crucial for guiding dietary protein recommendations for different genders and have significant clinical implications.

The ratio of alanine aminotransferase to high-density lipoprotein cholesterol is positively correlated with the insulin resistance in American adults: a population-based cohort study.

Previous studies have demonstrated a correlation between the ratio of alanine aminotransferase to high-density lipoprotein cholesterol (ALT/HDL-C) in the serum and the risk of diabetes. However, no existing study has investigated the association between insulin resistance (IR) and ALT/HDL-C. Therefore, this study aims to explore the association between ALT/HDL-C and IR in American adults. A total of 7,599 adults selected from the National Health and Nutrition Examination Survey (NHANES) in 2013 to 2020 were studied. IR was assessed based on the homeostatic model assessment of insulin resistance (HOMA-IR). And the association between IR and ALT/HDL-C was assessed through multiple logistic regression, generalized smooth curve fitting and subgroup analyses. Multiple logistic regression analysis indicated a significant correlation between IR and ALT/HDL-C, with odds ratios (OR) of 1.04 (95% CI = 1.02-1.05) in males and 1.04 (95% CI = 1.02-1.07) in females. A non-linear association and saturation effect between ALT/HDL-C and IR risk were identified, with an inverted L shaped curve and an inflection point at 33.62. The area under the ROC curve (AUC) of ALT/HDL-C was significantly larger (AUC = 0.725 for males and 0.696 for females, all p < 0.01) compared with the use of ALT, HDL-C, AST and AST/ALT. Subgroup analysis showed a significantly higher independent association in obese individuals and individuals aged ≥50 years (All P interaction <0.05). Elevated ALT/HDL-C demonstrates a significant correlation with IR, which can be used as a potential indicator of IR in American adults.

U-shaped relationship between non-high-density lipoprotein cholesterol and cognitive impairment in Chinese middle-aged and elderly: a cross-sectional study

BackgroundThe relationship between blood lipids and cognitive function has long been a subject of interest, and the association between serum non-high-density lipoprotein cholesterol (non-HDL-C) levels and cognitive impairment remains contentious.MethodsWe utilized data from the 2011 CHARLS national baseline survey, which after screening, included a final sample of 10,982 participants. Cognitive function was assessed using tests of episodic memory and cognitive intactness. We used multiple logistic regression models to estimate the relationship between non-HDL-C and cognitive impairment. Subsequently, utilizing regression analysis results from fully adjusted models, we explored the nonlinear relationship between non-HDL-C as well as cognitive impairment using smooth curve fitting and sought potential inflection points through saturation threshold effect analysis.ResultsThe results showed that each unit increase in non-HDL-C levels was associated with a 5.5% reduction in the odds of cognitive impairment (OR = 0.945, 95% CI: 0.897–0.996; p < 0.05). When non-HDL-C was used as a categorical variable, the results showed that or each unit increase in non-HDL-C levels, the odds of cognitive impairment were reduced by 14.2%, 20.9%, and 24% in the Q2, Q3, and Q4 groups, respectively, compared with Q1. In addition, in the fully adjusted model, analysis of the potential nonlinear relationship by smoothed curve fitting and saturation threshold effects revealed a U-shaped relationship between non-HDL-C and the risk of cognitive impairment, with an inflection point of 4.83. Before the inflection point, each unit increase in non-HDL-C levels was associated with a 12.3% decrease in the odds of cognitive impairment. After the tipping point, each unit increase in non-HDL-C levels was associated with an 18.8% increase in the odds of cognitive impairment (All p < 0.05).ConclusionThere exists a U-shaped relationship between non-HDL-C and the risk of cognitive impairment in Chinese middle-aged and elderly individuals, with statistical significance on both sides of the turning points. This suggests that both lower and higher levels of serum non-high-density lipoprotein cholesterol increase the risk of cognitive impairment in middle-aged and elderly individuals.

Microflexiblity and local integrability of horizontal curves

AbstractLet be an analytic bracket‐generating distribution. We show that the subspace of germs that are singular (in the sense of control theory) has infinite codimension within the space of germs of smooth curves tangent to . We formalize this as an asymptotic statement about finite jets of tangent curves. This solves, in the analytic setting, a conjecture of Eliashberg and Mishachev regarding an earlier claim by Gromov about the microflexibility of the tangency condition.From these statements it follows, by an argument due to Gromov, that the ‐principle holds for maps and immersions transverse to .

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

Study on the Application of Kramers-Kronig Relation for Polyurethane Mixture.

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers-Kronig (K-K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time-temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak-Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core-core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K-K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data.

Stress relaxation experimental research and prediction of GFRP pipes under ring deflection condition

Abstract Glass fiber-reinforced plastic (GFRP) pipes are widely used as buried pipes in petrochemical and other industries. At present, in-depth studies have been conducted on GFRP pipes in terms of internal hydrostatic pressure, axial compression, and cyclic internal pressure, especially limited research has been carried out on transverse load, especially stress relaxation behavior. In this study, GFRP pipes with three different component contents were subjected to different initial deflections at different temperatures and subjected to stress relaxation tests for 1000 h. The findings demonstrate that the stress relaxation behavior of GFRP pipes is not affected by the initial deflection. Rather, it is primarily influenced by temperature and sand entrapment content, which are identified as the key factors determining the stress relaxation behavior of GFRP pipes. In addition, the time-temperature superposition principle (TTSP) was used to pass the test results to obtain a smooth master curve and verify the applicability of TTSP on GFRP pipes. Subsequently, the relaxation performance of GFRP pipes was predicted after 50 years. This research result contributes to a more comprehensive understanding of the stress relaxation behavior of GFRP through accelerated testing and offers crucial insights into the application of GFRP pipes.