Triangular Method Research Articles

Territorial Production and Resource Structures of Asian Russia: Assessment, Typology, and Zoning

This article examines the territorial production and resource structures in the territory of Asian Russia, which include natural, economic, and social elements. The objective of this study is to assess, typologize, and zone the territorial production–resource structures. The methodological framework of this study is based on calculating an integral development indicator for the regions of Asian Russia, represented by an Adjusted Net Savings index. This index reflects regional wealth according to the World Bank’s expanded concept of national wealth, which includes three types of capital: “reproducible”, “natural”, and “human”. The study also involves a larger typology of the regions, classifying them based on the predominance of these capital forms through the Analytic Hierarchy Process and the triangular illustration method. Regional clustering within the study area was also conducted through the k-means method using Statistica 12 software. Accordingly, adjusted net savings and sectoral contributions to gross regional product were calculated for the regions in this area. A relationship between regional specialization and the level of genuine savings was identified, forming the basis for the grouping of regions. A total of three groups were distinguished: regions with negative, moderate, and the highest levels of genuine savings within the macroregion. A larger typology using dominant, predominant, and complex functions was also developed. Using data on natural, physical, and human capital in Asian Russia, its regions were clustered, resulting in the identification of five clusters. The territory was then zoned based on the clustering results. A total of eight zones were identified, reflecting the size and balance of the three types of capital (human, physical capital, and productive natural), with regions grouped according to their cluster membership and territorial proximity. The findings can help identify pathways for more sustainable development of this territory amidst evolving natural, economic, social, and geopolitical conditions.

Simulating and Verifying a 2D/3D Laser Line Sensor Measurement Algorithm on CAD Models and Real Objects.

The increasing adoption of 2D/3D laser line sensors in industrial and research applications necessitates accurate and efficient simulation tools for tasks such as surface inspection, dimensional verification, and quality control. This paper presents a novel algorithm developed in MATLAB for simulating the measurements of any 2D/3D laser line sensor on STL CAD models. The algorithm uses a modified fast-ray triangular intersection method, addressing challenges such as overlapping triangles in assembly models and incorporating sensor resolution to ensure realistic simulations. Quantitative analysis shows a significant reduction in computation time, enhancing the practical utility of the algorithm. The simulation results exhibit a mean deviation of 0.42 mm when compared to real-world measurements. Notably, the algorithm effectively handles complex geometric features, such as holes and grooves, and offers flexibility in generating point cloud data in both local and global coordinate systems. This work not only reduces the need for physical prototyping, thereby contributing to sustainability, but also supports AI training by generating accurate synthetic data. Future work should aim to further optimize the simulation speed and explore noise modeling to enhance the realism of simulated measurements.

[formula omitted]-conforming triangular spectral element method for quad-curl problems

In this paper, we consider the H(curl2)-conforming triangular spectral element method to solve the quad-curl problems. We first explicitly construct the H(curl2)-conforming elements on triangles through the contravariant transform and the affine mapping from the reference element to physical elements. These constructed elements possess a hierarchical structure and can be categorized into the kernel space and non-kernel space of the curl operator. We then establish H(curl2)-conforming triangular spectral element spaces and the corresponding mixed formulated spectral element approximation scheme for the quad-curl problems and related eigenvalue problems. Subsequently, we present the best spectral element approximation theory in H(curl2;Ω)-seminorms. Notably, the degrees of polynomials in the kernel space solely impact the convergence rate of the (L2(Ω))2-norm of uh, without affecting the semi-norm of H(curl;Ω) and H(curl2;Ω). This observation enables us to derive eigenvalue approximations from either the upper or lower side by selecting different degrees of polynomials for the kernel space and non-kernel space of the curl operator. Finally, numerical results demonstrate the effectiveness and efficiency of our method.

A Comparative Study of the Effects of Dumpsites on Groundwater Quality in Uyo Metropolis of Akwa Ibom State

The study was conducted to compare the effects of dumpsites on groundwater quality in Uyo Metropolis of Akwa Ibom State. It aimed at examining the effect of dumpsites from physicochemical and heavy metal content of borehole water and determining the water quality rating of boreholes in the study areas. Three (3) dumpsites, namely Uyo Village Road Dumpsite (UVD), Atiku Road Dumpsite (ARD) and Ediene Uyo Dumpsite (EUD) were used for the study. The triangular sampling method was used to select three boreholes in each dumpsite area, giving a total of thirty-six (36) samples on replication for the three dumpsites and control. The water samples were collected in well-labeled pretreated 1-litre plastic bottles and were immediately transported to the laboratory for analysis. Data obtained were analyzed using descriptive statistics and means of significant parameters were separated using the Duncan multiple range test at 5% level of probability. The result showed that mean pH was 7.49 in control, significantly lower than 8.22–8.66 in the study areas. Electrical conductivity was 245.33–580.67 μs/cm with 335.00 μs/cm as control. Mean temperatures were 28.53–28.67 oC and 28.0 oC for control. Also, values obtained for turbidity were 3.47–4.21 and 3.47 in control. DO in control borehole water was 3.07 mg/l while that of dumpsites was 3.18–3.37 mg/l. The calculated water indices were 1871.92, 33492.86 and 32288.10 for UVD, ARD and EUD respectively. The findings revealed that mean values in water quality parameters like Magnesium, Dissolved Oxygen, Lead, Cadmium, Nickel and Zinc were above the permissible limit of the World Health Organization for drinking water, indicating higher evidence of groundwater pollution in the study area. The study generally showed that borehole water samples from the three dumpsites were unsuitable for drinking. Public awareness among borehole owners and users within the dumpsite environment on ground water contamination by dumpsites was recommended among others in the study area and the water should be treated before human consumption.

Evaluating the Current Situation of River and Lake Shoreline Planning and Utilization Using an Improved Matter-Element Extension Model

Based on the analysis of the influencing factors of the current planning and utilization of river and lake shorelines, an index system of the current planning and utilization of river and lake shorelines is constructed. Based on the triangular fuzzy number method and the improved CRITIC method, the evaluation indicators are weighted and analyzed and then integrated to obtain the combined weight. An improved matter-element extension model was constructed to evaluate the current situation of shoreline planning and utilization in typical regions. At the same time, the TOPSIS evaluation model and the cloud theory evaluation model were compared and analyzed to verify the accuracy of the model. The improved matter-element model accounts for indicator incompatibility and the uncertainty of evaluation boundaries, offering a clearer reflection of the planning and utilization status.

A triangular acoustic emission source location method considering its anisotropic propagation behavior on the surface of finger-joint-laminated board

ABSTRACT To understand the anisotropic propagation characteristics of acoustic emission (AE) signals in finger-joint-laminated boards, an improved planar localization method for AE sources is proposed. Initially, the AE source was generated by the pencil-lead break (PLB) at a fixed position on the surface of the glued wood specimen, and two AE sensors were arranged in different directions at a fixed distance of 60 mm, and the AE propagation velocity was calculated according to the time difference of arrival (TDOA). For clarity, the grain parallel direction was defined as 0 degrees, with velocities measured every 10 degrees through a counterclockwise rotation. Using these measurements, two angular anisotropic wave velocity models were developed. Subsequently, three AE sensors arranged linearly on the specimen surface pinpointed the AE source’s location. This source location problem was formulated as a multi-parameter optimization model, constrained by the geometric relationships between the AE source and the sensors. A particle swarm optimization (PSO) algorithm was utilized to estimate the AE source’s angles relative to each sensor. The findings indicate that the located AE sources deviated by 6.0–19.0 mm from the predetermined PLB positions, with inaccuracies largely attributed to the anisotropic AE wave velocity models’ precision.

Sound waves tracing method in temperature–velocity coupling field of nuclear reactor

Turbulent coolant flow in a nuclear reactor’s primary loop leads to temperature non-uniformity in the heat pipe section. Utilizing sound wave temperature measurement techniques mitigates calculation errors caused by temperature variations. However, complex temperature–velocity coupling induces significant bending of sound wave paths, affecting measurement accuracy. This study proposes a triangular ray tracing method to accurately track sound wave paths considering coolant temperature gradients and flow dynamics. Experimental validation using finite element simulation data from the Hua-long Pressurized Reactor primary loop demonstrates improved reconstruction accuracy by up to 0.59% compared to straight lines and by up to 0.04% compared to other ray tracing methods.

Effects of yoga exercise on heart rate in post COVID-19 patients

Objective: The research aimed to study the effect of yoga exercise on heart rate in post-infected patients COVID-19. Methods: The participant group consisted of female post-Covid-19 patients aged 18–22 years at a university. Sukjai (Pseudonym), 20 people, all voluntarily signed a letter of consent. Systematic Random Sampling was performed, with the experimental group (EXG) (n=10) exercising with yoga for eight weeks, three days per day, 90 minutes per session. The control group (CG) (n=10) did not undergo any training. Quantitative data were collected, including heart rate before training and after the fourth and eighth weeks of training. Qualitative data were collected through semi-structured interviews. The data were analysed by checking their stability and trust using a triangular method. Results: It was found that (1) after exercising with yoga after week four and week eight, the experimental group had a mean heart rate that was significantly better than before training and better than the control group . (p<0.05). (2) yoga exercises for patients after COVID-19 infection improves heart rate. Conclusions: Yoga exercise improved the heart rate of patients with COVID-19. Therefore, maintaining the health of people of all ages is an alternative activity. Keywords: Yoga, Exercise, Heart rate, COVID-19,

Reliability Analysis of Subsea Riser System Based on Fuzzy Fault Tree Analysis Method

Abstract To deal with the complex structure of subsea riser system and the lack of failure statistics and insufficient information during operation, a fuzzy fault tree analysis (FFTA) method is applied to analyse the reliability of the subsea riser system, and a qualitative and quantitative analysis is carried out by establishing a fault tree model of the riser system to obtain the minimum set of cuts and the basic events. The fuzzy importance degree of each fundamental event is determined as well as the failure probability of the headline event of the fuzzy fault tree, “failure of subsea riser system,” using the triangular fuzzy number computation method. Finally, the “average value” method of comprehensive analysis of the fault tree model, the analysis results show that the bottom event riser check valve, riser buoyancy device, riser working medium isolation valve, riser line, riser gas lift device and other components of the failure of the subsea riser system is relatively the weak links, compared with the actual situation, the analysis results in line with the actual engineering situation, these five aspects should be regularly detected and focused on prevention. In conclusion, this research helps to comprehensively analyse the reliability of the riser system and take into account the uncertainty factors, and provides more accurate guidance on the reliability constraints for the localized design and production of subsea riser system.

On detection of BaO molecular lines in sunspot spectrum

ContextSpectral lines of diatomic molecules are perfect tools for studying the structure of sunspots and their temperature layers and magnetic sensitive absorption features, which are typically higher than in atomic lines. The integrated intensities of a few bands in the rotational structure of the astrophysically significant A1Σ+−X1Σ+and A′1Π−X1Σ+ systems of barium monoxide (BaO) have been measured experimentally using band spectra. An analysis of the prominent lines of (0, 0; 1, 1; 2, 2) bands of A1Σ+−X1Σ+transition and (0, 0; 1, 1; 2, 2) bands of A′1Π−X1Σ+transition with those of sunspot umbral spectrum. The effective rotational temperatures of the A′1Π−X1Σ+transition of BaO in the sunspot umbral spectrum are found to be in the range of 1600 K to 3200 K. AimsAn analysis of BaO prominent rotational molecular lines of A1Σ+−X1Σ+and A′1Π−X1Σ+transition with those of sunspot umbral spectral lines. To find the significant values of radiative transition parameters, vibrational temperature and the effective rotational temperature of the molecule in celestial objects. MethodsCalibrated the rotational structure of molecular band heads and lines for and A1Σ+−X1Σ+and A′1Π−X1Σ+ransitions in laboratory spectrum using most precise Hartmann's technique. High resolution FTS sunspot umbral spectra from NSO/Kitt Peak were used to detect rotational molecular lines due to the A′1Π−X1Σ+transition of the BaO molecule using the method of line coincidence. The effective rotational temperature was derived from the variation of equivalent width (W) with rotational quantum number (J) of spectrally well resolved rotational lines of a band in umbral spectrum. The triangular profile approximation method was used to estimate the equivalent width of the well resolved spectral lines. ResultsThe effective rotational temperatures of the A′1Π−X1Σ+transition of BaO in the sunspot umbral spectrum are found to be in the range of 1600 K to 3200 K. It is compared with other results with a view to obtaining useful physical parameters. This is an evidence to ascertain the possible presence of BaO molecule in solar spectrum in different layers. ConclusionsUnblended rotational lines due to the band of BaO, provide a good range of temperatures for the study of absorbing layers in umbral spectra. The A′1Π−X1Σ+transition of BaO molecular lines is found to be very sensitive to effective temperature. Radiative transition parameters data of these lines, in contrast to intensity measurements, provide us with more direct and detailed information to study the coolest parts of sunspot umbrae.

Modeling process for full forming sports underwear

Abstract Most of the sports underwear available is sewn using cutting and sewing techniques. During the exercise process, it is easy to cause discomfort to the skin due to repeated friction at the seam, and at the same time, it is also a waste of manpower and raw material costs. In order to address these issues present in existing sports underwear, during its design and development, combined with fully forming knitting technology, construction process model, so as to realize the integrated knitting of sports underwear. First of all, through the characteristics of the local style of sports underwear, the key points of its prototype were probed. Second, on this basis, its process model was established, including the forming methods and knitting rules of the body, shoulder collar, and bottom circumference. Finally, the feasibility of the technological model is proved by the braiding of a fully formed sports underwear. The change in the body size can be achieved by using the two-side braiding transfer method. The curve contour of the shoulder and neck can be obtained by using the triangular polyline segmentation method. The bottom part is divided into a cylinder part and a supporting part. The local braiding method is used to achieve the knitting. This study puts forward a process model and application method of fully formed sports underwear, which provides a certain method and reference for the design and production of fully formed sports underwear.

Improvements of the dynamics code TMSR3D for molten salt reactor leveraging triangular prism nodal method

Dynamic simulation with coupled model of neutronics/thermal-hydraulics (TH) is one of the crucial aspects in safety analysis for molten salt reactor (MSR), which requires a deeper insight into the interactions among hydrodynamics, heat transfer and neutron kinetics because of its special characteristics induced by fuel drift, in comparison to the traditional reactors using solid fuels. To improve the geometric adaptability and calculation precision of the MSR specific dynamics code TMSR3D based on quadrilateral nodal method and TH module including the multi-channel flow and single-channel heat transfer models, the analytic basis function expansion nodal (ABFEN) method using triangular prism nodes is implemented to solve the static neutron diffusion equations, an implicit backward difference method along with exponential transformation is adopted to deal with the neutron kinetics problems, and the concentration equations of delayed neutron precursors (DNP) considering fuel flow are solved by the method of characteristics. The VVER-440 transient benchmark is first selected to validate capacity of the updated code for simulating core with hexagonal assemblies. Subsequently, the Molten Salt Reactor Experiment (MSRE) is simulated for further validation, in which the steady-state characteristics including delayed neutron loss induced by circulating fuel, profiles of reactor temperature and DNP, impact of fuel residence time in external loop on the effective yields of delayed neutrons, two fuel pump driven transients, and the natural convection are analyzed and discussed in detail. The results agree well with that from similar codes and the experimental values, which indicate that the improvements conducted for TMSR3D are effective and correct.

Triangular Fuzzy Cognitive Maps Method for Modelling Interrelation between Causal and Trigger Factors Towards Students' Mathematics Problem-Solving Ability

The purpose of this study is to model the interrelation between causal and trigger factors towards students' mathematics problem-solving ability by using the triangular fuzzy cognitive maps (TrFCM) method. Selection weaknesses and limitations in the method of relational analysis cause the interrelation and influence between variables not to be visualised and do not reveal the characteristics of the actual interaction. As a result, this study demonstrates TrFCM as a more effective way of analysing the relationship between variables based on the complexity that happens in analysing causal factors and triggers for students' problem-solving abilities in mathematics. The results of the influential relations map (IRM) demonstrate that emotion and metacognition are the triggers for problem-solving ability. While executive function is the main cause of success in completing mathematics problems, it is also influenced by additional factors such as motivation, attention, and working memory. These causal and triggering factors also mobilise parts of students' cognitive and behavioural performance to improve the process of solving mathematics problems. Based on the outcomes of this study, computational intelligence methods like fuzzy systems give useful procedures for analysing data from expert surveys. The TrFCM method offers a more accurate relational analysis procedure in modelling interrelation between human factors.

A fourth order Runge-Kutta type of exponential time differencing and triangular spectral element method for two dimensional nonlinear Maxwell's equations

In this paper, we study a numerical scheme to solve the nonlinear Maxwell's equations. The discrete scheme is based on the triangular spectral element method (TSEM) in space and the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method in time. TSEM has the advantages of spectral accuracy and geometric flexibility. The ETD method involves exact integration of the linear part of the governing equation followed by an approximation of an integral involving the nonlinear terms. The RK4 scheme is introduced for the time integration of the nonlinear terms. The stability region of the ETDRK4 method is depicted. Moreover, the contour integral in the complex plan is utilized and improved to compute the matrix function required by the implementation of ETDRK4. The numerical results demonstrate that our proposed method is of exponential convergence with the order of basis function in space and fourth order accuracy in time.

Linear Time Train Contraction Minor Labeling for Railway Line Capacity Analysis

AbstractWhen no more than one train is feasibly contained in the separation headway times of two other trains, a triangular gap problem-based method is used to compute the consumed capacity in linear time. This is a strong condition limiting its applicability, while real-world operations often feature mixed traffic of various speeds, creating more complex structures beyond the characterization of a triangular gap. In this paper, we attempt to investigate the multi-train gap scenario and provide a general solution to the railway timetable structure and capacity analysis problem. Given a timetable, we use an incidence graph, the so-called train contraction minor, for representing the consecutive train operations and show that a longest path for spanning the compressed timetable is any path in a graph induced by some topological subsequence of trains that connects the predefined vertices in the train contraction minor. By vector-valued vertex labeling of this minor, we acquire an efficient algorithm that computes the consumed capacity of the timetable. Our algorithm runs in O(mn) time, where m and n are the number of trains and stations, respectively, and is free from the limitation and outperforms the near-linear time policy iteration implementation in the max-plus system of train operations. A toy example and a real-world case study demonstrate the effectiveness and computational performance of the proposed method. The proposed method based on train contraction minor contributes to the railway operations community by promoting the efficient computation of railway line capacity into linear time.

An Efficient Progressive Grid Generation Method Considering Internal Quality and Boundary Grid Adjustment

Due to its elegant appearance and high structural efficiency, free-form grid structures are increasingly adopted in architectural design. However, it is a challenging task for engineers to generate a uniform and well-shaped grid on a free-form surface while considering the processing of both interior and boundary of grid, especially for composite surfaces. To generate well-shaped grids with uniform rods, regular cells and smooth visual effects over free-form surfaces, this paper develops an innovative triangular grid generation method capable of automatically managing grid boundary with extending initial surface. In the method, nodes of grid structure are considered to be zero mass particles and are progressively added to the extended surface from geometric center to the boundary of surface. A boundary-processing algorithm is then established to evenly distribute nodes on initial boundary curve, while ensuring that grid cells at the boundary do not exhibit elongation. A mechanical simulation system based on spring-mass model is improved to optimize spatial grid structure, rods of grid are regarded as linear springs, a surface attraction force and an anchoring force are performed on grid nodes. Moreover, the proposed method allows architects change grid direction and rods length easily, which can greatly improve the efficiency of design. Several case studies show that the method can effectively avoid distortion of grids and generate well-shaped grids that can meet aesthetic requirements.

3D Geostatistical Modeling and Metallurgical Investigation of Cu in Tailings Deposit: Characterization and Assessment of Potential Resources

The management of mine tailings presents a global challenge. Re-mining these tailings to recover remaining metals could play a crucial role in reducing the volume of stored tailings, as historical mining methods were less efficient than those used today. Consequently, mine wastes have the potential to become unconventional resources for critical minerals. To assess this potential, critical minerals and metals in the mine tailings were investigated through sampling, characterization, and 3D geostatistical modeling. The Bleïda copper mine tailings in Morocco were modeled, and residual copper resources were estimated using ordinary kriging (OK). Tailings were systematically sampled at a depth of 1.8 m using a triangular grid and tubing method. The metallic and mineralogical content of the samples was analyzed, and a numerical 3D model of the tailing’s facility was created using topographic drone surveys, geochemical data, and geostatistical modeling. The results from the 3D block model of the Bleïda tailings facility reveal that the volume of deposited tailings is 3.73 million cubic meters (mm3), equivalent to 4.85 million tonnes (Mt). Furthermore, based on the average copper grade (~0.3% by weight) in the studied part of the tailings pond, the copper resources are estimated at 2760 tonnes. Mineralogical characterization indicates that this metallic content is mainly associated with sulfide and carbonate minerals, which exhibit a low degree of liberation. This study aims to serve as a reference for assessing the reprocessing feasibility of tailings in both abandoned and active mines, thereby contributing to the sustainable management of mine tailings facilities. Geostatistical modeling has proven effective in producing tonnage estimates for tailings storage facilities and should be adopted by the industry to reduce the technical and financial uncertainties associated with re-mining.

Super-Resolution Virtual Scene Rendering Technology Based on Generalized Huber-MRF Image Modeling

The traditional rendering technology creates virtual scenes with insufficient fidelity, which are quite different from real scenes. To address this issue, a super-resolution virtual scene rendering technology based on generalized Huber-MRF image modeling has been studied. This study preprocesses the original image through three steps: graying, filtering, and enhancement. The generalized Huber-MRF is employed for super-resolution image restoration to enhance image clarity. Corner features are extracted from the super-resolution image, and the Delaunay triangular grid method is used to construct the image's 3D model. Texture and lighting conditions of the virtual scene are then set through texture mapping, shadow rendering, and other technologies to achieve realistic scene effects. The results indicate that, when applied, the research technology yields a relatively small chamfer distance in virtual scene modeling, suggesting that the design method preserves the details and shape information of the original image, reducing the difference between the virtual scene and the real scene and increasing the fidelity of the virtual scene. Furthermore, this method achieves maximum PSNR and SSIM values of 17.54 and 0.978, respectively, with an image preprocessing time of only 1.21 s and a CPU utilization rate of only 35.5%. This method demonstrates excellent performance across multiple aspects.

Evaluation of mine ecological environment based on fuzzy hierarchical analysis and grey relational degree

In order to improve the level of mine ecological environment management and restoration, and to improve and enhance the overall environmental quality of mines. This study takes coal mine as the perspective, and constructs evaluation indexes in two steps, i.e., social network analysis method and relevant policy documents are combined to construct evaluation indexes. The indicator system contains 5 first-level indicators and 23 s-level indicators, and the triangular fuzzy number hierarchical analysis method is introduced to determine the comprehensive weight of each evaluation indicator, which overcomes the inadequacy of the objective empowerment method or the subjective empowerment method of single empowerment. The grey correlation analysis theory is used to establish a grey correlation evaluation model of mine ecological environment, which is applied to the evaluation of ecological environmental protection level of four coal mines in a province of China, making full use of the information of each index for quantitative evaluation, and finally obtaining the evaluated value of ecological environmental protection level of each coal mine. It is demonstrated that the evaluation model can make scientific and effective evaluation of the level of ecological environmental protection in mines. The study concludes that coal mines should pay attention to improving the comprehensive utilization rate of coal gangue in the next mine ecological environment management and restoration, and at the same time, reduce the ton of coal power consumption, ton of coal water consumption, and Increase in vegetation cover. This study provides a useful evaluation method for ecological environment management in mining areas, which is helpful to improve the quality of ecological management in mining areas.

Study on the preparation of high-concentration ammonium phosphate suspension fertilizer from wet-process phosphoric acid and its rheological properties

BackgroundNew water-soluble fertilizer can be applied to modern irrigation systems and has significant advantages. This study uses wet-process phosphoric acid as raw material and chelation and suspension technology to prepare water-soluble fertilizer containing high-concentration ammonium phosphate. MethodsFirst, the composition and viscosity of the wet-process phosphoric acid was analyzed, and the ammoniation and chelation processes were explored. Subsequently, four suspension formulations were compared and selected after product analysis. The final process conditions are: 42 wt % (P2O5 %) phosphoric acid, 20 wt % chelating agent, pH = 4.5, 0.03 wt % xanthan gum or 0.02 wt % carboxymethyl cellulose of respectively, and obtain suspension fertilizer by high-speed shearing. Significant FindsThe Bingham model and Casson model were used to fit the rheological data of the two, and R2 values were greater than 0.94. The thixotropic loops of the two were measured using the triangular shear rate variation method mode, and the Huang equation and MBM models were used to fit the thixotropic loop data of the two respectively. In addition, at different pH and temperature, the suspended fertilizer performed well.