Power Function Research Articles

Construction of Additive Allometric Biomass Models for Young Trees of Two Dominate Species in Beijing, China

The traditional volume-derived biomass method is limited because it does not fully consider the carbon sink of young trees, which leads to the underestimation of the carbon sink capacity of a forest ecosystem. Therefore, there is an urgent need to establish an allometric biomass model of young trees to provide a quantitative basis for accurately estimating the carbon storage and carbon sink of young trees. The destructive data that were used in this study included the biomass of the young trees of the two dominant species (Betula pendula subsp. mandshurica (Regel) Ashburner & McAll and Populus × tomentosa Carrière) in China, which was composed of the aboveground biomass (Ba), belowground biomass (Bb), and total biomass (Bt). Univariate and bivariate dimensions were selected and five candidate biomass models were independently tested. Two additive allometric biomass model systems of young trees were established using the proportional function control method and algebraic sum control method, respectively. We found that the logistic function was the most suitable for explaining the allometric growth relationship between the Ba, Bt, and diameter at breast height (D) of young trees; the power function was the most suitable for explaining the allometric growth relationship between the Bb and D of young trees. When compared with the independent fitting model, the two additive allometric biomass model systems provide additive biomass prediction which reflects the conditions in reality. The accuracy of the Bt models and Ba models was higher, while the accuracy of the Bb models was lower. In terms of the two dimensions—univariate and bivariate, we found that the bivariate additive allometric biomass model system was more accurate. In the univariate dimension, the proportional function control method was superior to the algebraic sum control method. In the bivariate dimension, the algebraic sum control method was superior to the proportional function control method. The additive allometric biomass models provide a reliable basis for estimating the biomass of young trees and realizing the additivity of the biomass components, which has broad application prospects, such as the monitoring of carbon stocks and carbon sink evaluation.

Effects of Dynamic Flow Rates on the In Vitro Bio-Corrosion Behavior of Zn-Cu Alloy

In the complicated real physiological environment in vivo, body fluids and blood are constantly replenished and move dynamically, and therefore, the dynamic impacts of bodily fluids and blood need to be considered in the evaluation of biodegradable materials. However, little research has been conducted on the impact of dynamic flowing circumstances on the corrosion characteristics of zinc-based alloys, particularly at high flow rates. The effects of various flow rates on the bio-corrosion behavior of the Zn-Cu alloy are thoroughly explored in this study. A model is developed using finite element analysis to investigate the impacts of flow rates and fluid-induced shear stress. The results reveal that the corrosion process of the Zn-Cu alloy is significantly accelerated by a higher flow rate, and a large fluid-induced shear stress caused by the boundary effect is found to promote corrosion. Furthermore, the empirical power function between the average flare rates in Hank’s solution and the corrosion rates of the Zn-Cu alloy is established by numerical simulation. The results provide insightful theoretical and experimental guidance to improve and evaluate the efficacy and lifespan of biomedical zinc-based alloy implants.

Biomimetic Slippery Surface with Exclusive Liquid-Repellent and Self-Cleaning Properties for Antifouling.

The nature always offers amazing inspiration, where it is highly desirable to endow coatings on marine equipment with powerful functions. An excellent example is slippery zone of Nepenthes pitcher, which possesses novel liquid-repellent and self-cleaning performance. Therefore, this study presents an efficient fabrication method to prepare a novel coating. The coatings were fabricated by designing biomimetic textures extracted from the lunate bodies of slippery zone on polydimethylsiloxane (PDMS) and then grafting Dictyophora indusiata polysaccharide (DIP) modifier. The as-prepared slippery coatings exhibited outstanding antifouling properties against kinds of daily life pollutants such as Chlorella and coffee. This synergistic strategy was proposed combined with environmentally friendly modifier grafting and heterogeneous microstructure on the surface to broaden new probabilities for manufacturing slippery coatings with incredible protective functionality.

A Cross-Sectional Study on Whether Comprehensively Gathering Information From Medical Records Is Useful for the Collection of Operational Characteristics.

This study tests whether comprehensively gathering information from medical records is useful for developing clinical decision support systems using Bayes' theorem. Using a single-center cross-sectional study, we retrospectively extracted medical records of 270 patients aged ≥16 years who visited the emergency room at the Tokyo Metropolitan Tama Medical Center with a chief complaint of experiencing headaches. The medical records of cases were analyzed in this study. We manually extracted diagnoses, unique keywords, and annotated keywords, classifying them as either positive or negative. Cross tables were created, and the proportion of combinations for which the likelihood ratios could be calculated was evaluated. Probability functions for the appearance of new unique keywords were modeled, and theoretical values were calculated. We extracted 623 unique keywords, 26 diagnoses, and 6,904 annotated keywords. Likelihood ratios could be calculated only for 276 combinations (1.70%), of which 24 (0.15%) exhibited significant differences. The power function+constant was the best fit for new unique keywords. The increase in the number of combinations after increasing the number of cases indicated that while it is theoretically possible to comprehensively gather information from medical records in this way, doing so presents difficulties related to human costs. It also does not necessarily solve the fundamental issues with medical informatics or with developing clinical decision support systems. Therefore, we recommend using methods other than comprehensive information gathering with Bayes' theorem as the classifier to develop such systems.

Functional changes in sleep-related arousal after ketamine administration in individuals with treatment-resistant depression

The glutamatergic modulator ketamine is associated with changes in sleep, depression, and suicidal ideation (SI). This study sought to evaluate differences in arousal-related sleep metrics between 36 individuals with treatment-resistant major depression (TRD) and 25 healthy volunteers (HVs). It also sought to determine whether ketamine normalizes arousal in individuals with TRD and whether ketamine’s effects on arousal mediate its antidepressant and anti-SI effects. This was a secondary analysis of a biomarker-focused, randomized, double-blind, crossover trial of ketamine (0.5 mg/kg) compared to saline placebo. Polysomnography (PSG) studies were conducted one day before and one day after ketamine/placebo infusions. Sleep arousal was measured using spectral power functions over time including alpha (quiet wakefulness), beta (alert wakefulness), and delta (deep sleep) power, as well as macroarchitecture variables, including wakefulness after sleep onset (WASO), total sleep time (TST), rapid eye movement (REM) latency, and Post-Sleep Onset Sleep Efficiency (PSOSE). At baseline, diagnostic differences in sleep macroarchitecture included lower TST (p = 0.006) and shorter REM latency (p = 0.04) in the TRD versus HV group. Ketamine’s temporal dynamic effects (relative to placebo) in TRD included increased delta power earlier in the night and increased alpha and delta power later in the night. However, there were no significant diagnostic differences in temporal patterns of alpha, beta, or delta power, no ketamine effects on sleep macroarchitecture arousal metrics, and no mediation effects of sleep variables on ketamine’s antidepressant or anti-SI effects. These results highlight the role of sleep-related variables as part of the systemic neurobiological changes initiated after ketamine administration. Clinical Trials Identifier: NCT00088699.

Modelling adult neurogenesis in the aging rodent hippocampus: a midlife crisis.

Contrary to humans, adult hippocampal neurogenesis in rodents is not controversial. And in the last three decades, multiple studies in rodents have deemed adult neurogenesis essential for most hippocampal functions. The functional relevance of new neurons relies on their distinct physiological properties during their maturation before they become indistinguishable from mature granule cells. Most functional studies have used very young animals with robust neurogenesis. However, this trait declines dramatically with age, questioning its functional relevance in aging animals, a caveat that has been mentioned repeatedly, but rarely analyzed quantitatively. In this meta-analysis, we use data from published studies to determine the critical functional window of new neurons and to model their numbers across age in both mice and rats. Our model shows that new neurons with distinct functional profile represent about 3% of the total granule cells in young adult 3-month-old rodents, and their number decline following a power function to reach less than 1% in middle aged animals and less than 0.5% in old mice and rats. These low ratios pose an important logical and computational caveat to the proposed essential role of new neurons in the dentate gyrus, particularly in middle aged and old animals, a factor that needs to be adequately addressed when defining the relevance of adult neurogenesis in hippocampal function.

ADAPTIVE CONTROL OF A SUBMARINE FOR VARIOUS DIVING DEPTHS USING AN EXPONENTIAL

Due to the progress of deep submergence capabilities, a submarine is extensively employed on many sides of marine science. For that reason, it has become necessary to design an effective submarine position controller while achieving a fast and stable mission. An adaptive analytical scheme for the underwater submarine was developed. The main purpose of the adaptive analytical scheme is to provide a powerful analytical controller that can successfully steer the submarine from the current state under the water to the surface of water in a short time. To achieve that, a seventh-term exponential function was proposed to reshape the reference diving depth while maintaining the control variable limitation and satisfying initial and final boundary conditions. The direct search method with two cascade loops was employed to achieve a minimum cost function by determining an appropriate constant of the function and minimum final time. However, using the direct search method can be time-consuming since a number of algebraic operations are executed inside these two loops. Therefore, the curve fitting method was used to fit the set of direct search method data using power functions. Then, at a certain diving depth, the function coefficients were computed based on the final settling time and function constant using the Gaussian elimination method. A nominal numerical simulation of the submarine’s model was implemented using both adaptive analytical and linear controllers.

Future changes in global rainfall erosivity: Insights from the precipitation changes

Quantifying future changes in rainfall erosivity is essential to address potential water erosion risks. This study reveals a significant power function relationship between rainfall erosivity and precipitation both globally and across various climatic zones. Building on this foundation, new empirical models were developed to project relative changes in rainfall erosivity. These models, predicted on the understanding that General Circulation Models (GCMs) provide more accurate predictions of climate change trends than exact meteorological values, utilizes the ratio of modeled historical precipitation to future precipitation under various scenarios as the variable, formulated as a power function. Data from three GCMs runs from both the Coupled Model Intercomparison Project phase 5 (CMIP5) and CMIP6–including historical, mid-term, and long-term periods–were employed. The analysis suggests that by the end of the 21st century, global annual rainfall erosivity could increase by 2.6% under the Shared Socio-Economic Pathway (SSP)1–2.6 scenario, by 3.5% under SSP2-4.5, and by a significant 6.4% under SSP5-8.5, relative to the 2000–2010 baseline. Furthermore, over 76% of the global land area is projected to experience an increase in rainfall erosivity over the century. Regions with projected changes in rainfall erosivity, whether increase or decrease, are likely to face more pronounced changes from mid-century onwards. The CMIP6 exhibits improved model consistency over its predecessor, CMIP5, indicating a greater water erosion risk as global warming progresses. These projections offer insights for strategies to combat soil degradation due to climate changes.

Screening transparent model fluids to emulate the rheological properties of high solid anaerobic digestate of food waste

Due to the opacity of high solid anaerobic digestate, optical visualization techniques (e.g., particle image velocimetry) cannot be used directly for measuring the flow field inside high solid anaerobic digestion (HSAD) systems. This study mainly focused on selecting suitable surrogate fluids for optical visualization techniques by comparing the flow curves, thixotropic properties, viscoelastic behavior and creep recovery properties of HSAD digestate with a total solid from 10 % to 15 % (w/w) and transparent model fluids. Results indicated that the Bingham model outperformed the power-law model and Herschel-Bulkley model in describing the flow curves of HSAD digestate, xanthan gum and laponite. The digestate and xanthan gum had a similar thixotropic kinetic coefficient of 0.003 and 0.004, respectively. Besides, the digestate and xanthan gum had a similar modulus transformation trend with a power function whose power exponents were 0.17 and 0.19, respectively. In general, xanthan gum can be a suitable substitute for HSAD digestate with a total solid from 10 % to 15 %. The results can guide the implementation of optical visualization techniques to understand the flow pattern within HSAD systems, and improve the mass and heat transfer efficiency during food waste disposal processes.

Dynamic Evolution of Infarct Volumes at MRI in Ischemic Stroke Due to Large Vessel Occlusion.

The typical infarct volume trajectories in stroke patients, categorized as slow or fast progressors, remain largely unknown. This study aimed to reveal the characteristic spatiotemporal evolutions of infarct volumes caused by large vessel occlusion (LVO) and show that such growth charts help anticipate clinical outcomes. We conducted a secondary analysis from prospectively collected databases (FRAME, 2017-2019; ETIS, 2015-2022). We selected acute MRI data from anterior LVO stroke patients with witnessed onset, which were divided into training and independent validation datasets. In the training dataset, using Gaussian mixture analysis, we classified the patients into 3 growth groups based on their rate of infarct growth (diffusion volume/time-to-imaging). Subsequently, we extrapolated pseudo-longitudinal models of infarct growth for each group and generated sequential frequency maps to highlight the spatial distribution of infarct growth. We used these charts to attribute a growth group to the independent patients from the validation dataset. We compared their 3-month modified Rankin scale (mRS) with the predicted values based on a multivariable regression model from the training dataset that used growth group as an independent variable. We included 804 patients (median age 73.0 years [interquartile range 61.2-82.0 years]; 409 men). The training dataset revealed nonsupervised clustering into 11% (74/703) slow, 62% (437/703) intermediate, and 27% (192/703) fast progressors. Infarct volume evolutions were best fitted with a linear (r = 0.809; p < 0.001), cubic (r = 0.471; p < 0.001), and power (r = 0.63; p < 0.001) function for the slow, intermediate, and fast progressors, respectively. Notably, the deep nuclei and insular cortex were rapidly affected in the intermediate and fast groups with further cortical involvement in the fast group. The variable growth group significantly predicted the 3-month mRS (multivariate odds ratio 0.51; 95% CI 0.37-0.72, p < 0.0001) in the training dataset, yielding a mean area under the receiver operating characteristic curve of 0.78 (95% CI 0.66-0.88) in the independent validation dataset. We revealed spatiotemporal archetype dynamic evolutions following LVO stroke according to 3 growth phenotypes called slow, intermediate, and fast progressors, providing insight into anticipating clinical outcome. We expect this could help in designing neuroprotective trials aiming at modulating infarct growth before EVT.

Analysis of impact pressure, rock-breaking effect, and ground vibration induced by the disposable CO2 fracturing tube

The technology of expansion fracturing with liquid CO2 (EFLCO2) has attracted increasing attention due to reduced vibration and damage. The disposable fracturing tube has been developed and is gradually replacing the Cardox tube. However, there is a lack of impact pressure testing of disposable tubes under real working conditions, selection of gas explosion design parameters, and systematic analysis of blasting vibration. This limitation has constrained the widespread application of disposable fracturing tubes in engineering. A joint monitoring of the pressure-time curves in the disposable tubes and boreholes was conducted. The rock-breaking effect of varying hole spacing parameters in the EFLCO2 design was analyzed, and a systematic study was carried out on the vibration peak value, frequency, and energy characteristics. The results show that (1) the pressure distribution characteristics, stress peak value, and duration in the disposable tubes are different from those of Cardox tubes, which show multi-peak distribution, low-pressure peak value, and short duration. The correlation between the pressure in the disposable tube, filling pressure, and liquid CO2 weight is established, and a theoretical calculation method for the borehole wall pressure is proposed; (2) The hole spacing in rocks of different hardness is suggested; and (3) At the same scale distance, the peak particle velocity (PPV) caused by EFLCO2 (PPVCO2) is significantly smaller than that caused by blasting (PPVexplosive). The ratio of PPVexplosive to PPVCO2 is a power function related to scale distance, and a distance-related zonality exist in this relationship. The frequency composition of the vibration signal caused by EFLCO2 is relatively simple with a narrow frequency band. Its PPV and energy are mainly concentrated in the low-frequency band. This research contributes to the optimization of disposable fracturing tubes, gas explosion design, and vibration hazard control.

Membrane capacitive deionization (MCDI): A flexible and tunable technology for customized water softening

There is a growing demand for water treatment systems for which the quality of feedwater in and product water out are not necessarily fixed with “tunable” technologies essential in many instances to satisfy the unique requirements of particular end-users. For example, in household applications, the optimal water hardness differs for particular end uses of the supplied product (such as water for potable purposes, water for hydration, or water for coffee or tea brewing) with the inclusion of specific minerals enhancing the suitability of the product in each case. However, conventional softening technologies are not dynamically flexible or tunable and, typically, simply remove all hardness ions from the feedwater. Membrane capacitive deionization (MCDI) can potentially fill this gap with its process flexibility and tunability achieved by fine tuning different operational parameters. In this article, we demonstrate that constant-current MCDI can be operated flexibly by increasing or decreasing the current and flow rate simultaneously to achieve the same desalination performance but different productivity whilst maintaining high water recovery. This characteristic can be used to operate MCDI in an energy-efficient manner to produce treated water more slowly at times of normal demand but more rapidly at times of peak demand. We also highlight the “tunability” of MCDI enabling the control of effluent hardness over different desired ranges by correlating the rates of hardness and conductivity removal using a power function model. Using this model, it is possible to either i) soften water to the same hardness level regardless of the fluctuation in hardness of feed waters, or ii) precisely control the effluent hardness at different levels to avoid excessive or insufficient hardness removal.

A distortion model test method of the casing string system considering FSI

To solve the problem of prototype test’s high cost and difficulty of the casing string system in shale gas horizontal wells, this paper proposes a large-scale distortion model test method for the casing string system. Firstly, the elastic centralizer is simplified as elastic support, and the dynamic model of casing string system is established by finite element method. Then, the test platform of casing string system is designed and built. The modal test results show that the maximum error of the first five natural frequencies between the numerical calculation and the test results is 5.12 %, which verifies the correctness of the dynamic model of casing string system. On this basis, the distortion model’s constant power similarity law (CPSL) and power function similarity law (PFSL) are obtained by the dimensional analysis method and the least square method. The CPSL and PFSL are used to predict the vibration characteristics of the prototype casing string system by distortion models with different scaling ratios. The calculation and analysis show that the prediction accuracy of the PFSL is higher than CPSL’s with the same scaling ratio, and the PFSL can accurately predict natural frequency of the prototype casing string system within a large-scale distortion range and greatly reduce the test cost.

Standardizing differential scanning calorimetry (DSC) thermal decomposition temperatures at various heating rates of an energetic material as a threshold one

Differential scanning calorimetry (DSC) test is capable of providing comprehensive data of peak temperature (Tp, K) and onset temperature (To, K) at various heating rates (β) and widely applied in the thermal safety assessment of energetic materials (EMs). However, Tp and To (Tp/o) are variable, depending on β, making inconvenience and confusion in thermal stability of different EMs, in particular, in the case of testing conditions absent. This study aims to standardize Tp/o at various β to Tp/o,β→0 as a threshold temperature of thermal decomposition. It is confirmed that Pow2P2 (two-parameter power function) is feasible to fit the Tp/o−β relationship by any two experimental points, and extrapolate Tp/o,β→0. Thereby, Tp/o,β→0, as a single value of DSC test of one EM, benefits for thermal stability study.

Study on Numerical Simulation of Large-Diameter Borehole Pressure Relief in Deep High-Gas Soft Coal Seams.

The deep highly gassy soft coal seam has the characteristics of high ground stress, high gas pressure, and low permeability. In the process of coal roadway excavation, there are problems such as frequent gas concentration exceeding the limit and easy induction of gas dynamic disasters. To investigate the pressure relief and disaster reduction efficiency of large-diameter boreholes in a deep high-gas soft coal seam, the 8002 high-gas working face of the Wuyang coal mine was taken as the engineering background to study the deformation law of large-diameter boreholes in deep high-gas soft coal seams. A coupled damage-stress-seepage model for pressure relief of large-diameter boreholes in gas-bearing coal seams was constructed based on the Hoek-Brown criterion, the correlation between the damage area and the gas pressure distribution in the gas-bearing coal seam after the pressure relief of boreholes of different apertures was analyzed, and the pressure relief efficiency of different technical parameters "three flower holes" in the roadway head was determined. The law of stress transfer, gas migration, and energy release in the coal seam after pressure relief of a large-diameter borehole under different initial gas pressures was revealed, and the power function equations of the damage range and borehole diameter, maximum stress at the roadway head, and driving distance after pressure relief of a gas-bearing coal seam were determined. Results showed that under the confining pressure of the 8002 working face roadway in the Wuyang coal mine, the pressure relief effect of 250 mm aperture is better, the drilling plastic zone is "butterfly" or "X″-type distribution, and the plastic zone range is positively correlated with the aperture size. Under the arrangement of "three flower holes", the plastic zone is larger and the pressure relief effect is better when the hole spacing is 1.4 m. With the increase of initial gas pressure, the vertical stress above the borehole increases and the pressure relief efficiency decreases. According to the vertical stress distribution within 200 h of borehole pressure relief, the pressure relief process is divided into a coal damage and failure stage, stress balance stage, and hole collapse stability stage. The research results provide a theoretical basis for the prevention and control of coal rock gas dynamic disasters by large-diameter drilling in a deep high-gas soft coal seam.

Ultrasound-assisted extraction of alginate from Ecklonia maxima with and without the addition of alkaline cellulase – factorial and kinetic analysis

Ultrasound-assisted extraction and enzyme-assisted extraction are two methods that can be employed to recover valuable compounds from seaweeds at milder operating conditions than conventional chemical extraction methods. The aim of the study was to determine whether pH, enzyme addition and extraction temperature significantly impacted extraction of alginate from Ecklonia maxima in the presence of ultrasonication and to model extraction kinetics. Firstly, a 23 factorial experimental design was employed at constant sonication rate, with pH (8 and 10), temperature (50 and 60 °C), and enzyme-to-substrate ratio (E:S 0 and 1 %) as the independent variables. Secondly, extraction kinetics of alginate were investigated at different extraction conditions, through fitting of the Peleg and Power models. Highest extraction for alginate was achieved at pH 10, 60 °C, E:S = 0 % within the first 60 min of extraction. The addition of enzyme improved solubilised dry matter content, but it had a less clear impact on the alginate yield. Both the Peleg (R2 = 0.893 – 0.997) and Power function (R2 = 0.861 – 0.987) models provided good fit to the experimental data and can used to describe extraction kinetics of alginate during combined ultrasound-enzymatic assisted extraction.

Research on damage behavior of silicone rubber under dynamic impact

Viscoelastic rubber materials are widely used in various vibration reduction structures of military and construction machinery. The complex driving and working conditions make the mechanical structure suffer severe impact, which leading to the damage or lose efficacy of the important viscoelastic elements. In order to reveal the dynamic mechanical properties of silicone rubber after impact, the Uniaxial compression tests of silicone rubber under different high strain rates were carried out with the separated Hopkinson pressure bar (SHPB) dynamic impact experiment, and the original Zhu-Wang-Tang (ZWT) constitutive model was modified by combining logarithmic law and power function law. The dynamic impact simulation model of silicone rubber was established using the modified ZWT-rate-dependent constitutive model, and the dynamic impact damage behavior of silicone rubber was studied under the condition of high strain rate, and the microscopic damage analysis was carried out on the experimental silicone rubber samples by scanning electron microscopy (SEM). The results show that the silicone rubber has obvious strain rate effect and strong deformation resistance at high strain rate. The modified ZWT-rate-dependent constitutive model can be used to obtain the constitutive expression of unified parameters, which can better describe the dynamic mechanical properties of silicone rubber at high strain rates. After dynamic impact compression, a damage line zone appears in the silicone rubber sample. There is a certain rule between the position of the line zone and the loading strain rate and the friction coefficient of the end face, and the silicone rubber is significantly affected by the friction effect of the end face.

Biomass Allocation of China’s Forests as Indicated by a Literature-Based Allometry Database

Allometry reflects the quantitative relationship between the allocation of resources among different organs. Understanding patterns of forest biomass allocation is critical to comprehending global climate change and the response of terrestrial vegetation to climate change. By collecting and reorganizing the existing allometric models of tree species in China, we established a database containing over 3000 empirical allometric models. Based on this database, we analyzed the model parameters and the effect of climate on forest biomass allocation under the context of ‘optimal allocation theory’. We showed that (1) the average and median exponent of power functions for above-ground biomass were 2.344 and 2.385, respectively, which significantly deviated from the theoretical prediction of 2.667 by metabolic theory (p &lt; 0.01). (2) The parameters of the allometric model were not constant, and not significantly correlated with temperature, precipitation, latitude, and elevation (p &gt; 0.05), but were more closely related to individual size (p &lt; 0.01). (3) Among different types of forests, the proportion of above-ground biomass in tropical rainforests and subtropical evergreen rainforests was significantly higher than that in temperate forests and boreal forests (p &lt; 0.05). The proportion of trunk and branch biomass allocated to tropical rainforest was significantly higher than that of boreal forest (p &lt; 0.05), while the proportion of root and leaf biomass allocated to tropical rainforest was significantly lower than that of boreal forest (p &lt; 0.05). (4) The abiotic environment plays a crucial role in determining the allocation of plant biomass. The ratio of below-ground/above-ground biomass is significantly and negatively correlated with both temperature and rainfall (p &lt; 0.01), and significantly and positively correlated with altitude and latitude (p &lt; 0.01). This means that as temperature and rainfall increase, there is a decrease in the amount of biomass allocated to below-ground structures such as roots. On the other hand, as altitude and latitude increase, there is an increase in below-ground biomass allocation. These findings highlight the importance of considering the influence of abiotic factors on plant growth and development.

A note on a q-difference equation related to Riccati equations

In this paper, we consider the existence of analytic solutions of associated with q-Airy equation y ( q 2 t ) + qty ( qt ) − y ( t ) = 0. By the position of q, we study the existence of analytic solutions of the form of power functions, the convergence radius of the formal solutions for some cases is also given.

КОМП'ЮТЕРНЕ МОДЕЛЮВАННЯ ЕЛЕКТРИЧНИХ ПРОЦЕСІВ ПІД ЧАС ВИНИКНЕННЯ ЧАСТКОВИХ РОЗРЯДІВ У СУЧАСНІЙ ПОЛІМЕРНІЙ ІЗОЛЯЦІЇ СИЛОВИХ КАБЕЛІВ

A Simulink model of modern polymer insulation of power cables with a spherical gas micro-inclusion, in which high-frequency partial discharges (PDs) occur, has been developed. The magnitude of the voltage both at the beginning of the PD appearance and during its decay was taken into account during numerical calculations and research of such threshold electro-physical processes as PD in solid polymer insulation. The dependence of the voltage drop on the gas micro-inclusion on its size, as well as the time interval between discharges, which is necessary for the formation of free electrons in this gas micro-inclusion, as a necessary condition for the appearance of the next PD, was also taken into account. Based on the results of the calculations, the electro-physical dependences that occur during the PD, such as the influence of the size of the inclusion, the amplitude and frequency of the applied sinusoidal voltage on the above-mentioned characteristics were investigated. It has been revealed that with an increase in the diameter d of a gas mi-croinclusion, such characteristics as the number of discharges per period and the charge of one PD also increase, and this charge increases in proportion to a power function . When the voltage on the cable insulation increases, the number of PDs per period increases, which causes an increase in other characteristics, and when the frequency of the applied voltage increases, the average value of the PDs current increases almost proportionally to the increase in this frequency. Having obtained the results of the calculation of the level of PDs that occur when high-frequency voltage is applied, it is possible to obtain results for the main characteristics of PDs that occur at other frequencies, in particular at the industrial frequency of 50 Hz, which will make it possible to predict the technical condition of the insulation in terms of the residual resource of its trouble-free operation. References 18, figures 6, table 1.