Homogeneous Coefficients Research Articles

A phantom study on the applicability of a detectability index in ultrasound imaging

The assessment of clinical image quality on ultrasound is currently often subjective. While image quality factors such as contrast response or depth of penetration can be evaluated semi-automatically, the evaluation of high contrast resolution requires test objects with specific inserts. The aim of this study was to evaluate the applicability of image quality metrics which were derived from Linear System Theory in the field of medical ultrasound imaging. Modular Transfer Function (MTF) and noise power spectrum (NPS) were determined on four phantoms. Image quality was assessed using a detectability index for different diameters. One phantom contained a cylinder filled with water, which appears as a circle in the US images. The other three phantoms were homogeneous and consisted of three different materials all based on PVA (polyvinyl alcohol). The basic phantom material was a 10% PVA hydrogel. The two other materials included microplastic spheres and starch to increase echogeneity. NPS and the MTF were determined using MATLAB routines. Two linear US transducers with bandwidths of 2.4–10 and 4–15 MHz were used to show the dependence of the index on the principal frequency of the US wave. The results show that for all phantom materials and object sizes (1–10 mm diameter), the detectability indices decreased with increasing penetration depth (from 6 to 10 cm). In addition, all indices of the higher frequency transducer were higher than those of the lower frequency transducer. When comparing the different phantom materials (PVA, PVA with starch and PVA with microspheres), different mean pixel value (MPV) were found, while the standard deviations for the materials were similar. This enabled us to evaluate the detectability index at different signal-to-noise ratios (SNR). Measures of image homogeneity (coefficient of the variance and variation) showed no significant difference to a commercial phantom (p-values ranging from 0.16 to 1, average p-value 0.5). These results suggest that the concept of a detectability index can also be applied to US imaging.

Non-Communicable Diseases and Non-Modifiable Risk Factors: Analysis of the Situation in Three Ecuadorian Cities, 2023

Introduction: noncommunicable diseases (NCDs) have become the main causes of morbidity and mortality worldwide and their incidence and prevalence is increasing. Objective: to analyze nonmodifiable risk factors for NCDs in Azogues, Biblián and Déleg. Methodology: observational, descriptive-correlatonial study in a probabilistic sample of 993 people (men and women), over 20 years of age, residents of District 03D01, applying the survey technique, through a validated questionnaire for the detection of disease risk factors chronic-degenerative. Statistical analysis was performed in the Jamovi software, using nonparametric tests such as Chi-square of homogeneity and other coefficients to measure the effect size "Cohen's d" and the strength of association "Cramer's V". Results: median age 39 years, women (69.1%), "mestizos" (99.4%), from rural areas (64.8%), with secondary education (47.4%), married (59.9%), hypertensive (32%), diabetics (12%), chronic respiratory disease (10%), thyroid disease (5%), heart disease (2%), cancer (1%), overweight/obesity (56%), dyslipidemias (23%). Conclusions: Nonmodifiable factors such as age, ethnicity, sex and family history are determining factors in the development of NCDs, and in District 03D01 they are significantly associated (p<0.05), especially with diabetes and arterial hypertension.

Uncertainty quantification analysis of bifurcations of the Allen–Cahn equation with random coefficients

In this work we consider the Allen–Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we introduce a random coefficient in the linear reaction part of the equation, thereby accounting for random, spatially-heterogeneous effects. Importantly, we assume a spatially constant, deterministic mean value of the random coefficient. We show that this mean value is in fact a bifurcation parameter in the Allen–Cahn equation with random coefficients. Moreover, we show that the bifurcation points and bifurcation curves become random objects. We consider two distinct modeling situations: (i) for a spatially-homogeneous coefficient we derive analytical expressions for the distribution of the bifurcation points and show that the bifurcation curves are random shifts of a fixed reference curve; (ii) for a spatially-heterogeneous coefficient we employ a generalized polynomial chaos expansion to approximate the statistical properties of the random bifurcation points and bifurcation curves. We present numerical examples in 1D physical space, where we combine the popular software package Continuation Core and Toolboxes (COCO) for numerical continuation and the Sparse Grids Matlab Kit for the polynomial chaos expansion. Our exposition addresses both dynamical systems and uncertainty quantification, highlighting how analytical and numerical tools from both areas can be combined efficiently for the challenging uncertainty quantification analysis of bifurcations in random differential equations.

Numerical study of the effects of loading parameters on high-energy gas fracture propagation in layered rocks with peridynamics

The objective of this study is to investigate the influence of loading parameters on the propagation pattern of high-energy gas fractures in layered rock formations. To this end, a peridynamic model for brittle rock accounting for material heterogeneity was proposed. The ability of the model to simulate dynamic fractures was validated through laboratory experiments, and the homogeneity coefficient for the critical elongation rate was calibrated. On this basis, a numerical model of high-energy gas fracturing in layered rocks containing interfaces was constructed. Simulations were conducted to analyse high-energy gas fracturing from cylindrical intact boreholes and perforated boreholes under varying loading parameters. The results indicate that as the loading rate increases, the number of radial fractures surrounding the borehole gradually increases, whereas the influence of in-situ stress on fracture propagation diminishes. When the loading rate is fixed, both an increase in the peak pressure and a decrease in the decay rate are conducive to enhancing the propagation length of fractures. The propagation speed of fractures significantly decreases when they reach an interface but recovers after they penetrate it. Fractures tend to penetrate an interface when the angle of approach is closer to a right angle, and the direction of fracture propagation can be controlled through a perforation design. These findings provide valuable insights into the selection and optimization of loading parameters for reservoir stimulation via high-energy gas fracturing.

Refined Prediction Method for Production Performance of Deep-Water Turbidite Sandstone Oilfield: A Case Study of AKPO in Niger Delta Basin, West Africa.

Deep-water oilfields frequently employ large or superlarge well spacing, leading to significant production dynamics influenced by reservoir factors. Traditional methodologies often disregard these influences, resulting in poor accuracy. Therefore, an enhanced prediction methodology rooted in reservoir characteristics is proposed. This approach introduces the dynamic relative permeability law as a bridge, capturing macroscopic oil/water movement within the reservoir. For the first time, it integrates production dynamics with key controlling reservoir factors, encompassing reservoir architecture, injection-production connectivity, and reservoir heterogeneity. The results indicate that (1) In deep-water turbidite sandstone fields with ultralarge injector-producer well spacings, the distribution of oil-water movement is primarily influenced by reservoir connectivity and heterogeneity. The injection water sweeping ability coefficient can quantitatively describe the water flooding capacity, with a strong negative correlation between the injection water sweeping ability coefficient and interwell nonconnectivity coefficient and reservoir homogeneity coefficient. This suggests that better reservoir connectivity or weaker heterogeneity results in stronger water flooding capacity, leading to a wider range of water flooding under the same injection volume. (2) For regions with strong water flooding capacity (injection water sweeping ability coefficient 0.30-0.80), the water-free production period is the main production stage, with a focus on improving the planar flooding conditions. For regions with poor water flooding capacity (injection water sweeping ability coefficient 0.00-0.10), the middle and late water-cut periods are the main production stages, with a focus on improving interlayer dynamic differences in the later stages. For regions with moderate water flooding capacity (injection water sweeping ability coefficient 0.10-0.30), the initial focus should be on expanding planar flooding, followed by a focus on improving interlayer dynamic differences in the later stages. (3) The dynamic relative permeability law, capable of comprehensively portraying the reservoir's influence on macroscopic oil/water movement, emerges as a rational choice for production performance prediction in such contexts. Our method can improve the accuracy, compared with traditional method without geographical factors, from 45% to 90% during water-cut rising stage and 31% to 81% during production declining stage. The high prediction accuracy (90%) observed in the AKPO oilfields underscores the method's efficacy in directing on-site optimization and adjustments for the development of deep-water turbidite sandstone oilfields.

A Numerical Analysis of the Non-Uniform Layered Ground Vibration Caused by a Moving Railway Load Using an Efficient Frequency–Wave-Number Method

The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory model is proposed to quickly obtain the numerical results without losing accuracy. The track is regarded as a composite Euler–Bernoulli beam resting on the layered ground, and the spatial heterogeneity of the ground soil is considered. The ground dynamic characteristics of an elastic, layered, non-uniform foundation are investigated, and numerical results at three typical train speeds are reported based on the developed Fortran computer programs. The results show that as the soil homogeneity coefficient increases, the peak acceleration continuously decreases in the transonic case, while it gradually increases in the supersonic case, and the ground acceleration spectrum at a far distance obviously decreases; the maximum acceleration occurs at the track edge, and a local rebound in vibration attenuation occurs in the supersonic case.

Robust Integrative Analysis via Quantile Regression with Homogeneity and Sparsity

Integrative analysis plays a critical role in integrating heterogeneous data from multiple datasets to provide a comprehensive view of the overall data features. However, in multiple datasets, outliers and heavy-tailed data can render least squares estimation unreliable. In response, we propose a Robust Integrative Analysis via Quantile Regression (RIAQ) that accounts for homogeneity and sparsity in multiple datasets. The RIAQ approach is not only able to identify latent homogeneous coefficient structures but also recover the sparsity of high-dimensional covariates via double penalty terms. The integration of sample information across multiple datasets improves estimation efficiency, while a sparse model improves model interpretability. Furthermore, quantile regression allows the detection of subgroup structures under different quantile levels, providing a comprehensive picture of the relationship between response and high-dimensional covariates. We develop an efficient alternating direction method of multipliers (ADMM) algorithm to solve the optimization problem and study its convergence. We also derive the parameter selection consistency of the modified Bayesian information criterion. Numerical studies demonstrate that our proposed estimator has satisfactory finite-sample performance, especially in heavy-tailed cases.

Parameters of ISO 4037 wide spectrum X-ray reference field

The parameters of the ISO-4037 wide spectrum (W-series) X-ray reference fields were simulated using the SpekPy web-based simulation software. One of the most important physical quantities (air Kerma rate) and other radiation quantities (X-ray fluence spectrum and its averaged energy, the first and the second half value layers, as well as the beam homogeneity coefficient) were also deduced. The comparison in radiation quantities between the simulated (obtained from this work) and the ISO-published data was performed to confirm the reliability of SpekPy simulations (the maximum discrepancy between them was less than 4.0%). The air Kerma rate trend as a function of the W-series X-ray reference field was investigated and presented in this work. The values of air Kerma rates can be applied in calibrations of wide-spectrum X-ray measuring devices.

Current Issues of Methodology of Wholesale Turnover Analysis

Wholesale trade is the buying and selling of products in large volume. Products are purchased in bulk from manufacturers and then delivered to retail stores. The transfer of goods from the sphere of production to the sphere of consumption is called commodity circulation. Merchandise turnover, in turn, is divided into wholesale and retail turnover. As a rule, due to the conditions of production and circulation, goods must go through the intermediate links of production, turnkey and trade in order to be brought directly from the production to the consumer. The operations of buying and selling goods between intermediate links are called wholesale turnover. As a result of wholesale turnover, the goods do not yet pass into the sphere of personal consumption, they continue to circulate in the sphere of circulation, are transferred to the disposal of some retail trade or industrial processing, and then again participate in the circulation of goods. Thus, in order to bring goods into the retail trade network, intermediary links are needed, which carry out wholesale goods turnover. These are mainly distributors, who play a major role in the organization of goods circulation in the shortest way to bring goods to the retail network, speed up their turnover and reduce circulation costs. It is possible that the manufacturer supplies the goods to the retail store himself and does not have an intermediary (distributor) engaged in wholesale trade. In the conditions of the market economy, the study of the issues of perfecting the wholesale and retail turnover analysis methodology is one of the topical topics, since these two forms of business (wholesale and retail trade) are important intermediaries of the marketing channel, and in the absence of these two links, the entire chain will fail. Keywords: wholesale turnover, retail turnover, price index, volume index, dynamic line, growth rate, trend, sales forecast, coefficient of variation, mean square deviation, coefficient of homogeneity.

ISO 4037 narrow spectrum X-ray reference field: Simulation and measurement

The paper presents the characteristics of the ISO-4037 narrow spectrum X-ray reference fields in 02 different manners: simulation using the SpekPy and measurement using a calibrated ionization chamber. The physical (air Kerma rate) and radiation (X-ray fluence-spectrum-averaged energy, the first and the second half value layers, as well as the beam homogeneity coefficient) quantities were simulated using the SpekPy web-based simulation toolkit. In addition, air Kerma rates were measured by the ionization chamber. The characteristics of the ISO-4037 narrow spectrum X-ray reference fields were determined for various X-ray beam qualities (i.e., N-40, 60, 80, 100, 120, and 150) at 250 cm from the X-ray focal spot. The air Kerma rate tendency was deduced by comparing simulation and measurement data. The combined standard uncertainty of measured air Kerma rate was investigated and presented.

Prediction, mapping, and implication for better soil organic carbon management in Ethiopia

AbstractA precise soil organic carbon (SOC) content estimate is crucial soil quality parameter for agricultural produce and ecological safety. Moreover, geospatial modeling of SOC is critical when there are limited laboratory equipment and chemical reagents for soil analysis. This study used geostatistics—ordinary kriging (OK) and inverse distance weighting (IDW)—to map SOC in Libokemkem area, Northwest Ethiopia, for improved SOC management. About 107 soil samples were obtained from the plow layer at a 20‐cm depth and SOC was determined. Statistical Package for Social Sciences version 24.0 was used to generate descriptive statistics, and geostatistical analysis was also performed on the data using ArcGIS platform. The coefficient of determination (R2) and root mean square error (RMSE) derived from the validation of the predicted maps were used to assess the models. The results revealed homogeneity (coefficient of variation < 10%), low (0.12%–1.74%), and optimal (1.74%–4.06%) mean levels of SOC in study area. The OK showed an R2 of 0.74 and an RMSE of 13%, and the IDW revealed an R2 of 0.69 and an RMSE of 14%. The semivariogram results indicate a moderate dependence for SOC with stable, circular, spherical, exponential, and Gaussian models. We conclude that the sustainable monitoring of SOC is significant in enhancing soil quality. However, further study considering all drivers of spatial variability for SOC in the study and other soil sampling approaches improving performance of the prediction models is needed.

Characteristics of the reference X-ray narrow-spectrum series at SSDL of Institute for Nuclear Science and Technology

This paper presents the characteristics of the reference X-ray narrow-spectrum series used in the Secondary Standard Dosimetry Laboratory (SSDL) at Institute for Nuclear Science and Technology (INST) with X-ray beam irradiator. In order to perform calibration works, it is highly important to verify the characteristics and qualities of reference X-ray beam recommended by the International Standardization Organization (ISO) 4037:2019. The characteristics of the X-ray beams in terms of the half-value layer, homogeneity coefficient and the air kerma rate are determined for the narrow-spectrum series in the 40 and 150 keV range. The related dosimetric quantities such as the ambient dose equivalent and personal dose equivalent also determined. The experimental values are well consistent with the recommended values of the ISO 4037 criteria. It implies that the reference X-ray narrow-spectrum series (N-series) can be applied in calibration works of X-ray measuring devices used in radiation safety assessment.

Economic tolerance design of the P2 raceway based on the quasi-static model of aerospace ball bearings

This study focused on designing the raceway tolerance of high-precision rolling bearings. After the tolerance error equivalence relationship is defined, the application of the rolling bearing error equalization effect in tolerance design is studied. First, a five-degree of freedom quasi-static model was established for angular contact ball bearings. The waviness was included in the manufacturing error, and the radial and axial runouts of the bearing inner ring were calculated. Second, the error homogenization effect of the rolling bearing was studied, and the error homogenization coefficient was defined. The results of the study demonstrated that the bearing rotary accuracy was higher than the raceway error by an order of magnitude. Third, the manufacturing error range of each precision grade of the rolling bearing raceway was obtained by investigating errors of the equalization coefficient. Finally, the specific value of the raceway tolerance of P2 rolling bearings was obtained.

Static In-Line Gas Mixer for Physiological Capnogram Simulation

For the simulation of a physiological capnogram with a lung simulator it is important to homogenize CO2 in the expiratory air adequately with a mixing element, while being limited in size and energy consumption. We design and test static in-line mixers based on helical blade (Kenics) design and crossbars (SMX) design for optimized homogenization of CO2 in air. We investigate the effect of design variations such as element length and number on gas homogenization and pressure loss coefficient ζ. With the chosen assessment method, we find that the SMX design mixer provides the best compromise between homogenization and pressure loss.

Gray Level Homogeneity Analysis: A Novel Approach

In this article, we propose a method that helps us to analyze the homogeneity of gray levels locally by calculating a coefficient for each pixel based on the nature of neighboring pixels. This principle of encoding pixels according to their adjacent neighbors is described the nature of the distribution of gray levels within the image and measures their degree of homogeneity locally. This allows us to detect the different regions of the image and their contours based on the coefficient of homogeneity of the gray levels. In addition, this allows us to exploit these homogeneity coefficients to restructure regions of the image, extract and enhance the image contours while reducing the noise present in the image. This homogeneity study principle has several functions in the study and analysis of image texture, as do other methods of homogeneity assessment, such as the local contrast descriptor (LCD) and the co-occurrence matrix.

Modelling rock fracturing by a novel implicit continuous to discontinuous method

This research introduces a novel implicit continuous to discontinuous method to investigate the cross-scale failure process of discontinuous rock masses, including fine fracture creation, propagation, and rigid block contact. This method enables an intact rock to split and crush, with the local deformation/movement propagating rapidly throughout the whole system. The method was applied to investigate the progressive slope failure. The results revealed that the number of failure elements within the slope increased rapidly at the primary fracture stage. The upper part of the failure band gradually shifted upward and backward towards the slope crest, where several tension cracks were clearly visible. Additionally, the failed zone became wider as the homogeneity coefficient m increased. Furthermore, the factor of safety (FoS) increased as the growth stage of m progressed, but it reached a constant value when m exceeded 8, indicating that the material became relatively uniform. Interestingly, for slopes with varying elevation heights, the FoS decreased in a power function form as the ratio of the slope height to the width of the slope top surface increased. Overall, these findings shed light on developing the continuous-discontinuous computational model, with the application to study the progressive failure process of slopes.

Forest Structure of Pinus ayacahuite in Southern Mexico

Spatial structure refers to the horizontal and vertical arrangement of individual trees, and the most accurate way to describe it within a community is to characterize tree strata in terms of their dimensions. The aim of this study was to determine the horizontal and vertical structure of pure stands of Pinus ayacahuite Ehrenb. ex Schltdl., in forests of southern Mexico. Forest measurement data from 24 sample plots were used. For analysis of the horizontal structure, diameters within a range of 0.20 cm to 77 cm were used, while for the vertical structure, heights were from 0.09 m to 40.9 m. Non-parametric histograms and Kernel density methods were used in the analysis, and Fisher and Marron multimodality tests were performed. The homogeneity of the forest stands was determined by the coefficient of homogeneity, and the vertical and horizontal structures were described using the stratification proposed by Pretzsch. The results indicate that the horizontal structure corresponds to a diameter distribution with a reversed "J" shape in 79.2% of the sample plots, while 91.8% of the sites were classified as irregular with coefficients of homogeneity of 1.0 to 3.0. In the vertical structure, it was observed that the lower stratum predominated in 75% of the plots, while 25% had a higher concentration of individuals in the middle stratum. The upper stratum had accumulation percentages ranging from 1.3% to 33.3% but did not predominate in any of the plots. According to the multimodality tests, 50% of the plots present multimodality in the horizontal structure, while in the vertical structure this condition is present in 38% of the plots. Knowledge of the spatial structure of Pinus ayacahuite forest stands is essential to define silvicultural strategies that ensure the sustainable functioning of the ecosystem in terms of yield continuity and conservation.

Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville–Gel’fand problem

We determine the second term of the asymptotic expansions for the first m eigenvalues and eigenfunctions of the linearized Liouville–Gel’fand problem associated with solutions that blow-up at m points. Our problem is the case with an inhomogeneous coefficient in a two-dimensional domain and we extend the previous studies for the problem with a homogeneous coefficient. We also discuss in detail the required regularity of the coefficient necessary to reach the conclusion.

Nachal'no-kraevye zadachi dlya odnorodnykh parabolicheskikh sistem v poluogranichennoy ploskoy oblasti i uslovie dopolnitel'nosti

We consider initial–boundary value problems for homogeneous parabolic systemswith coefficients satisfying the double Dini condition with zero initial conditions in a semiboundedplane domain with nonsmooth lateral boundary. The method of boundary integralequations is used to prove a theorem on the unique classical solvability of such problems in thespace of functions that are continuous together with their first spatial derivative in the closureof the domain. An integral representation of the obtained solutions is given. It is shown thatthe condition for the solvability of the posed problems considered in the paper is equivalent tothe well-known complementarity condition.

JUSTIFICATION OF THE DESIGN AND TECHNOLOGICAL PARAMETERS OF THE ROTOR MIXER OF PERIODIC ACTION COMBINED FEED

The last stage of preparation of fodder mixtures is mixing of components with the help of special devices - mixers of continuous or periodic action. From the point of view of zootechnics, it is important not only to include in the fodder mixture the components provided for by the diet in the required ratio, but also to ensure an even distribution of all components throughout the volume of the mixture. The homogeneity of the mixture ensures the same nutritional value of the feed in all parts of its volume. Currently, when creating a new generation of mixers for dry fodder mixtures, preference is given to rotating mixers. The advantages of mixers of this type compared to stationary intermittent mixers of any type are: a reduction in feed unloading time, a fully automated chamber cleaning cycle, the absence of stagnant zones and rubbing parts. The purpose of the research is to determine the rational structural and technological parameters of the intermittent rotary mixer and to study the change in the homogeneity of the mixture when varying their values. Research was conducted in two stages: numerical modeling and experimental research. Numerical simulation was implemented in the Simcenter Star-CCM+ software package. As research factors, we accept the following parameters: angle of inclination of the blade α (0 °, 45 °, 90 °), mass of material m (0.1 kg, 0.2 kg, 0.3 kg), rotation frequency n (30 rpm min, 60 rpm, 90 rpm), mixing duration t (1 min, 3 min, 5 min). Experimental studies were carried out on a laboratory installation of a periodic rotary mixer. As a result of numerical modeling and experimental studies of the mixing process in a rotary mixer of batch feed, the dependences of the change in the homogeneity coefficient of the mixture in the mixer h on the angle of inclination of the blade α, the mass of the material m, the rotation frequency n, and the duration of mixing t were established. By fulfilling the condition of maximizing the homogeneity of the mixture in the Wolfram Cloud software package, the rational parameters of the rotary compound feed mixer of periodic action were obtained: α = 50.5 °, t = 4.415 min., m = 0.11 kg, n = 43.9 rpm. At the same time, the homogeneity coefficient is h = 0.98.