The dataset is originated, conceived, designed and maintained by Xiaoke WANG, Zhiyun OUYANG and Yunjian LUO. To develop the China's normalized tree biomass equation dataset, we carried out an extensive survey and critical review of the literature (from 1978 to 2013) on biomass equations conducted in China. It consists of 5924 biomass equations for nearly 200 species (Equation sheet) and their associated background information (General sheet), showing sound geographical, climatic and forest vegetation coverages across China. The dataset is freely available for non-commercial scientific applications, provided it is appropriately cited. For further information, please read our Earth System Science Data article (https://doi.org/10.5194/essd-2019-1), or feel free to contact the authors.

The Supporting Information includes derivations of equations for analytic approximations to the biphasic response function in terms of model sigmoid equations (Appendix A). In addition, transformation equations are given for parameter values that enforce a normalization between sigmoid and biphasic concentration-response functions (Appendix B). Fig A illustrates the sigmoid-like components of the positive and negative affectors composing the biphasic response function. Fig B illustrates the relative error between the sigmoid-like approximations for the left- and right-hand sides of the biphasic response and the full biphasic response. Fig C conceptualizes the ad hoc normalization method. Fig D illustrates how the sigmoid and biphasic response functions could be compared. Table A provides parameter values for the plots shown in Fig B. (PDF)

BackgroundLeft ventricular mass normalization for body size is recommended, but a question remains: what is the best body size variable for this normalization—body surface area, height or lean body mass computed based on a predictive equation? Since body surface area and computed lean body mass are derivatives of body mass, normalizing for them may result in underestimation of left ventricular mass in overweight children. The aim of this study is to indicate which of the body size variables normalize left ventricular mass without underestimating it in overweight children.MethodsLeft ventricular mass assessed by echocardiography, height and body mass were collected for 464 healthy boys, 5–18 years old. Lean body mass and body surface area were calculated. Left ventricular mass z-scores computed based on reference data, developed for height, body surface area and lean body mass, were compared between overweight and non-overweight children. The next step was a comparison of paired samples of expected left ventricular mass, estimated for each normalizing variable based on two allometric equations—the first developed for overweight children, the second for children of normal body mass.ResultsThe mean of left ventricular mass z-scores is higher in overweight children compared to non-overweight children for normative data based on height (0.36 vs. 0.00) and lower for normative data based on body surface area (-0.64 vs. 0.00). Left ventricular mass estimated normalizing for height, based on the equation for overweight children, is higher in overweight children (128.12 vs. 118.40); however, masses estimated normalizing for body surface area and lean body mass, based on equations for overweight children, are lower in overweight children (109.71 vs. 122.08 and 118.46 vs. 120.56, respectively).ConclusionNormalization for body surface area and for computed lean body mass, but not for height, underestimates left ventricular mass in overweight children.

The Saha equation describes the relative number density of consecutive ionization levels of a given atomic species under conditions of thermodynamic equilibrium in an ionized gas. Because the number density in the denominator may be very small, special steps must be taken to ensure numerical stability. In this paper we recast the equation into a form in which each ionization fraction is normalized by the total number density of the atomic species, analogous to the Boltzmann equation describing the distribution of excitation states for a given ion.

EMG data were normalized using Max-Min strategy. For comparison across all subjects, ʃIEMG values were normalized through following formula. the result of this equation ranged all the ʃIEMG values in to -1 to +1 ʃIEMGN = ʃIEMGi / ʃIEMGMAX

Normalized lift LN equations for different lift-generating systems.

International Journal of Social Studies and public policy

All three types of SIF-driven T models integrate canopy conductance (gc) with the Penman-Monteith model, differing in how gc is derived: from a SIFobs driven semi-mechanistic equation, a SIFsunlit and SIFshaded driven semi-mechanistic equation, and a SIFsunlit and SIFshaded driven machine learning model.

The difference between a simplified SIF-gc equation and a SIF-gc equation is the treatment of some parameters and is shown in https://doi.org/10.1016/j.rse.2024.114586.

In this dataset, the temporal resolution is 1 day, and the spatial resolution is 0.2 degree.

BL: SIFobs driven semi-mechanistic model

TL: SIFsunlit and SIFshaded driven semi-mechanistic model

hybrid models: SIFsunlit and SIFshaded driven machine learning model.

The first column of the table provides the names of the methods used to combine -values investigated in our study. The second column lists the reference number cited in this paper for the publication (Ref) corresponding to the method used. The third column provides the equation number for the method distribution function used to compute the formula -value. The fourth column indicates if a method equation can accommodate (acc.) weight when combining -value. The fifth column gives the normalization (nor.) procedure used to normalize the weights. Finally, the last column conveys the information about a method's capability to account for correlation (corr.) between -values.

Abstract The Poincaré code is a Maple project package that aims to gather significant computer algebra normal form (and subsequent reduction) methods for handling nonlinear ordinary differential equations. As a first version, a set of fourteen easy-to-use Maple commands is introduced for symbolic creation of (improved variants of Poincaré’s) normal forms as well as their associated normalizing transformations. The software is the implementation by the authors of carefully studied and followed up sele...

Title of program: POINCARÉ Catalogue Id: AEPJ_v1_0

Nature of problem Computing structure-preserving normal forms near the origin for nonlinear vector fields.

Versions of this program held in the CPC repository in Mendeley Data AEPJ_v1_0; POINCARÉ; 10.1016/j.cpc.2013.04.003

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

PH FORMULA CORPUS V1

PH_FORMULA_CORPUS_V1 is a large-scale formula corpus containing 160 million normalized mathematical expressions. Each formula has been carefully normalized to ensure concise, consistent, and simplified representations.

  🗓️ Timeline

✅ July 2025 – Released the formula corpus 🔜 Aug 2025 – Upcoming release of the synthetic datasets ⏳ Sep 2025 – Scheduled release of a model achieving commercial-grade qualit PHOCR

  🔧 Normalization Process… See the full description on the dataset page: https://huggingface.co/datasets/puhuilab/ph_formula_corpus_v1.

We characterize the textural and geochemical features of ocean crustal zircon recovered from plagiogranite, evolved gabbro, and metamorphosed ultramafic host-rocks collected along present-day slow and ultraslow spreading mid-ocean ridges (MORs). The geochemistry of 267 zircon grains was measured by sensitive high-resolution ion microprobe-reverse geometry at the USGS-Stanford Ion Microprobe facility. Three types of zircon are recognized based on texture and geochemistry. Most ocean crustal zircons resemble young magmatic zircon from other crustal settings, occurring as pristine, colorless euhedral (Type 1) or subhedral to anhedral (Type 2) grains. In these grains, Hf and most trace elements vary systematically with Ti, typically becoming enriched with falling Ti-in-zircon temperature. Ti-in-zircon temperatures range from 1,040 to 660°C (corrected for a TiO2 ~ 0.7, a SiO2 ~ 1.0, pressure ~ 2 kbar); intra-sample variation is typically ~60-15°C. Decreasing Ti correlates with enrichment in Hf to ~2 wt%, while additional Hf-enrichment occurs at relatively constant temperature. Trends between Ti and U, Y, REE, and Eu/Eu* exhibit a similar inflection, which may denote the onset of eutectic crystallization; the inflection is well-defined by zircons from plagiogranite and implies solidus temperatures of ~680-740°C. A third type of zircon is defined as being porous and colored with chaotic CL zoning, and occurs in ~25% of rock samples studied. These features, along with high measured La, Cl, S, Ca, and Fe, and low (Sm/La)N ratios are suggestive of interaction with aqueous fluids. Non-porous, luminescent CL overgrowth rims on porous grains record uniform temperatures averaging 615 ± 26°C (2SD, n = 7), implying zircon formation below the wet-granite solidus and under water-saturated conditions. Zircon geochemistry reflects, in part, source region; elevated HREE coupled with low U concentrations allow effective discrimination of ~80% of zircon formed at modern MORs from zircon in continental crust. The geochemistry and textural observations reported here serve as an important database for comparison with detrital, xenocrystic, and metamorphosed mafic rock-hosted zircon populations to evaluate provenance.

This paper introduces the integration of the Cobb-Douglas (CD) utility model with quantum computation, utilizing the Clairaut-type differential formula. We propose a novel economic-physical model using envelope theory to establish a direct link with quantum entanglement, thereby defining emergent probabilities in the optimal utility function for two goods within a given expenditure limit. The study illuminates the interaction between the CD model and quantum computation, emphasizing the elucidation of system entropy and the role of Clairaut differential equations in understanding the utility's optimal envelopes and intercepts. Innovative algorithms utilizing the 2D-Clairaut differential equation are introduced for the quantum formulation of the CD function, showcasing accurate representation in quantum circuits for one and two qubits. Our empirical findings, validated through IBM-Q computer simulations, align with analytical predictions, demonstrating the robustness of our approach. This methodology articulates the utility-budget relationship within the CD function through a clear model based on envelope representation and canonical line equations, where normalized intercepts signify probabilities. The efficiency and precision of our results, especially in modeling one- and two-qubit quantum entanglement within econometrics, surpass those of IBM-Q simulations, which require extensive iterations for comparable accuracy. This underscores our method's effectiveness in merging economic models with quantum computation.

The Arctic has warmed nearly four times faster than the global average since 1979, resulting in rapid glacier retreat and exposing new glacier forelands. These forelands offer unique experimental settings to explore how global warming impacts ecosystems, particularly for highly climate-sensitive arthropods. Understanding these impacts can help anticipate future biodiversity and ecosystem changes under ongoing warming scenarios. In this study, we integrate data on arthropod diversity from DNA gut content analysis—offering insight into predator diets—with quantitative measures of arthropod activity density at a Greenland glacier foreland using Structural Equation Modelling (SEM). Our SEM analysis reveals both bottom-up and top-down controlled food chains. Bottom-up control, linked to sit-and-wait predator behavior, was prominent for spider and harvestman populations, while top-down control, associated with active search behavior, was key for ground beetle populations. Bottom-up controlled dynamics predominated during the early stages of vegetation succession, while top-down mechanisms dominated in later successional stages further from the glacier, driven largely by increasing temperatures. In advanced successional stages, top-down cascades intensify intraguild predation (IGP) among arthropod predators. This is especially evident in the linyphiid spider Collinsia holmgreni, whose diet included other linyphiid and lycosid spiders, reflecting high IGP. The IGP ratio in C. holmgreni negatively correlated with the activity-density of ground-dwelling prey, likely contributing to the local decline and possible extinction of this cold-adapted species in warmer, late-succession habitats where lycosid spiders dominate. These findings suggest that sustained warming and associated shifts in food web dynamics could lead to the loss of cold-adapted species, while brief warm events may temporarily impact populations without lasting extinction effects. Methods Data CollectionData were collected using wet pitfall traps established across various patches within the Qassi glacier foreland and supplemented with data retrieved from the GEM (Global Ecological Monitoring) database for Kobbefjord. The specific timelines for data collection are as follows:

Qassi 2015 Sampling:

Wet pitfall traps were set up on July 8, 2015, and continuous sampling occurred until August 7, 2015. Sampling was interrupted due to rainy weather and resumed from August 12 to August 20, 2015.

Qassinnguit 2016 Sampling:

Wet pitfall traps were established on July 6, 2016, with continuous sampling until August 5, 2016. After a pause due to rain, sampling continued from August 10 to August 19, 2016.

Soil samples were collected at Qassi on August 7, 2015, and at Qassinnguit on August 5, 2016, to characterize environmental variables, specifically measuring soil water content and organic matter during dry weather conditions. NDVI (Normalized Difference Vegetation Index) measurements were taken on August 1, 2016, to assess vegetation biomass across the sampled patches. Data Retrieval for KobbefjordData for Kobbefjord were retrieved from the GEM database, which provided existing ecological data relevant to the study, allowing for a comparative analysis of predator-prey interactions across different environments. These data are shared under CC BY-SA 4 but are not included here. Access to GEM data may be requested via https://data.g-e-m.dk/. Arthropod Identification and AnalysisCaptured arthropods were identified to species or family level using standard taxonomic keys and references. COI barcoding was performed to enhance the reference library used for metabarcoding of predator gut contents. Most specimens were barcoded at the Canadian Centre for DNA Barcoding (CCDB), employing primers LCO1490 and HCO2198. Sanger sequencing of the amplicons was conducted, and the sequences were deposited in BOLD and GenBank. The density of arthropods was quantified based on the number of individuals captured in the pitfall traps. Soil samples underwent analysis to determine water and organic matter content. Gut Content AnalysisThe gut contents of arthropod predators collected during the study were analyzed using molecular techniques to determine the composition of their prey community. DNA metabarcoding was employed to identify various prey species present in the guts of predators, including linyphiid spiders, harvestmen, and ground beetles. This analysis provided critical insights into the trophic linkages between predators and their prey, supporting the understanding of predator-prey dynamics in the context of environmental changes. Data TransformationsFor statistical analysis, the following transformations were applied to the data:

Intraguild predation (IGP) ratios were arcsine and square root transformed to meet the assumptions of normality for statistical tests. Distance to the glacier snout and time since deglaciation were log-transformed to stabilize variance and normalize the data distribution. Arthropod activity densities were also log-transformed for the same reasons. NDVI values were utilized without transformation, reflecting their original measurement values.

Qassi and Qassinnguit Dates and Sampling Information

Soil Sampling Dates: August 7, 2015 (Qassi) and August 5, 2016 (Qassinnguit).

NDVI Scanning Date: August 1, 2016.

Wet Pitfall Trap Setup:

Qassi 2015: July 8 to August 7, resumed August 12 to August 20. Qassinnguit 2016: July 6 to August 5, resumed August 10 to August 19.

The primary aim of this study is to explore the influence of social media on university students’ revisit intention in sports tourism, using Expectation-Confirmation Model and the Uses and Gratifications Theory. A structured questionnaire was distributed to a random sample of 435 students from three universities in Hubei Province to measure their self-reported responses across six constructs: perceived usefulness, information quality, perceived enjoyment, electronic word-of-mouth (eWOM), satisfaction, and revisit intention. Employing a hybrid approach of Structural Equation Modeling (SEM) and Artificial Neural Networks (ANN), the study explains the non-compensatory and non-linear relationships between predictive factors and university students’ revisit intention in sports tourism. The results indicate that information quality, perceived enjoyment, satisfaction, and eWOM are significant direct predictors of revisit intention in sports tourism. In contrast, the direct influence of perceived usefulness on revisit intention is insignificant. ANN analysis revealed the normalized importance ranking of the predictors as follows: eWOM, information quality, satisfaction, perceived enjoyment, and perceived usefulness. This study not only provides new insights into the existing literature on the impact of social media on students’ tourism behavior but also serves as a valuable reference for future research on tourism behavior.

Stable isotope data analyzed in the manuscript. (XLSX)

The primary aim of this study is to explore the influence of social media on university students’ revisit intention in sports tourism, using Expectation-Confirmation Model and the Uses and Gratifications Theory. A structured questionnaire was distributed to a random sample of 435 students from three universities in Hubei Province to measure their self-reported responses across six constructs: perceived usefulness, information quality, perceived enjoyment, electronic word-of-mouth (eWOM), satisfaction, and revisit intention. Employing a hybrid approach of Structural Equation Modeling (SEM) and Artificial Neural Networks (ANN), the study explains the non-compensatory and non-linear relationships between predictive factors and university students’ revisit intention in sports tourism. The results indicate that information quality, perceived enjoyment, satisfaction, and eWOM are significant direct predictors of revisit intention in sports tourism. In contrast, the direct influence of perceived usefulness on revisit intention is insignificant. ANN analysis revealed the normalized importance ranking of the predictors as follows: eWOM, information quality, satisfaction, perceived enjoyment, and perceived usefulness. This study not only provides new insights into the existing literature on the impact of social media on students’ tourism behavior but also serves as a valuable reference for future research on tourism behavior.

The dataset is the normalized burnt ratio (NBR) products of 2022 over the Tibetan Plateau. The dataset is produced based on Landsat surface reflectance dataset. It is calculated by the NBR equation which uses the difference ratio between the NIR band and SWIR1 band to enhance the feature of the burned area. And the corresponding production of quality identification documents (QA) is also generated to identify the cloud, ice and snow. NBR is usually used to extract burned area information effectively, and to monitor the vegetation restoration in burned area.

Nomenclature and symbols.

For each explanatory variable the expected LVM values are calculated twice. First, based on a predictive equation developed for the OVER subgroup, next on a predictive equation developed for the NORM subgroup. In order to compare these linear regression coefficients differences between the paired expected LVM values were calculated and linear regression coefficients for the relationship between the differences and BMI z-score were tested.