Quadratic Polynomial Research Articles

Optimization of process parameters for polishing aero-engine blade with abrasive cloth wheel considering spindle vibration and polished roughness

The vibration of machine tool spindle is very important for machining. Firstly, in order to explore the relationship between spindle vibration and process parameters, the spindle vibration acceleration when polishing aero-engine blade was measured, and the quadratic polynomial models between the spindle vibration acceleration in X, Y and Z direction and the process parameters were established. Secondly, a quadratic polynomial model for the influence of process parameters on polished surface roughness was also determined. Thirdly, through the Analysis of Variance (ANOVA) and main effect analysis, it can be seen that the spindle speed has the greatest impact on the vibration. Finally, a multi-objective optimization model was established with the optimization objective of minimizing spindle vibration acceleration and polished surface roughness, and the optimal process parameters were solved using genetic algorithm. The optimal process parameters were verified and the results show that the polished surface roughness with the optimal process parameters are all less than 0.4 μm, and the deviation rates between the theoretical optimization results of spindle vibration acceleration and the experimental results are all less than 10%, indicating that the optimization results are good.

Equilibrium measures on Julia sets of random quadratic polynomials

Abstract We consider sequences of compositions of quadratic polynomials f c n ( z ) = z 2 + c n . For such sequences one can naturally generalise the definitions of the Julia set and basin of infinity from the autonomous case. In this setting the Julia set depends on a sequence ω = ( c 0 , c 1 , … ) . We study the equilibrium (harmonic) measure on such Julia sets. In particular, we calculate the Hausdorff dimension of the equilibrium measure and study its dependence on the ‘scale of randomnes’.

Short communication: Estimation of the dietary standardized ileal digestible valine to lysine ratio required for 40 to 130 kg pigs during the finisher periods

BackgroundThree experiments were conducted separately to determine the optimum standardized ileal digestible (SID) valine (Val) to lysine (Lys) ratio for early finishing (Experiment 1, 40 to 75 kg bodyweight), finishing (Experiment 2, 75 to 100 kg bodyweight), and late finishing (Experiment 3, 100 to 130 kg bodyweight) pigs. Dietary SID Val: Lys ratios were designed at 0.61, 0.65, 0.69, 0.73, and 0.77. The optimal SID Val: Lys ratio was estimated by different regression models, including a quadratic polynomial model, a two-slope quadratic broken-line model, a curvilinear-plateau model, and a one-slope straight broken-line model.ResultsIn Exp.1, a total of 550 early finishing pigs (initially 40.3 kg bodyweight) were used in a 38-day growth trial. Pigs consuming 0.61 dietary SID Val: Lys ratio had lower final bodyweight compared to those fed 0.69 in diets. Using regression models, the optimal dietary SID Val: Lys requirement for average daily gain (ADG) was between 0.63 and 0.68, and for feed to gain ratio (F: G) was between 0.62 and 0.68, respectively. In Exp.2, 525 finishing pigs (initially 76.4 kg) were used in a 26-day trial. Based on regression models, estimate of the required SID Val: Lys for ADG was between 0.65 and 0.71, and for F: G was between 0.64 and 0.70, respectively. In Exp.3, 640 late finishing pigs (102 kg bodyweight) were used in a 27-day trial. No significant improvement was found for performance parameters of pigs from 100 to 130 kg, while 0.73 SID Val: Lys ratio resulted in the highest ADG and the lowest F: G from a numerical point of view.ConclusionsThese findings indicated that the optimum SID Val: Lys requirement for pigs from 40 to 75 kg was between 0.62 and 0.68, and for pigs from 75 to 100 kg was estimated to be between 0.64 and 0.71, using different regression models.

Optimizing the content of Li2CO3, Na2SO4 and TEA in fly ash–cement system by response surface methodology

With an optimized dosage, hardening accelerators become a vital means of modifying fly ash-cement system (FAC). This study comprehensively investigated the mechanical properties of FAC modified by Li2CO3, Na2SO4, and triethanolamine (TEA) under different dosages, and optimized the dosage of accelerators through the response surface method (RSM). The synergistic effect of accelerators on the hydration of FAC was characterized by thermogravimetric differential scanning calorimetry (TG-DSC), X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). The results demonstrated that the factors and response value followed a quadratic polynomial model. The regression coefficients R2 of the model were all greater than 0.9, indicating good agreement with the experimental data. The content of Li2CO3 and Na2SO4 had an extremely significant effect on the compressive strength of 1d and 3d, followed by TEA. The optimal mix ratio predicted by RSM was 0.12% Li2CO3, 0.47% Na2SO4, and 0.40% TEA. Early hydration stages revealed that the combined action of these accelerators increased the formation of CH, CaCO3, and amorphous C-(A)-S-H gel. Microscopically, the surface of fly ash exhibited alkali-induced corrosion, thereby enhancing its pozzolanic reactivity.

Characteristics of constant pressure dehydrogenation and construction of linear diffusion model for solid hydrogen storage materials: A case study of TiMn1.5 alloy

Solid-state hydrogen storage is considered to be the most promising hydrogen storage technology because of its high volumetric capacity and good security. The process of hydrogenation and dehydrogenation of solid hydrogen storage materials can be characterized by a diffusion kinetic model, which can be used to guide the safe and efficient application of hydrogen storage materials. Currently, experimental study on the dehydrogenation characteristics under constant pressure outer boundary condition has not been carried out methodically, and a simple and reliable diffusion kinetic model under this condition should be established based on the experimental results. In this study, an experimental platform for hydrogen absorption and constant pressure dehydrogenation of solid hydrogen storage materials was independently established. The TiMn1.5 alloy and its interstitial hydrides were taken as the experimental research objects to conduct constant pressure dehydrogenation tests, and the dehydrogenation properties at different temperatures were systematically studied. The results show that the dehydrogenation rate decreases with the increase of testing time. The ultimate capacity of hydrogen release increases first and then decreases with the increasing temperature, reaching the maximum value at 30 °C. It is found that the diffusion coefficient increases linearly with time during constant pressure dehydrogenation process. On this basis, a linear diffusion kinetic model is established. The initial diffusion coefficient D0 calculated by the new model has a quadratic polynomial relationship with temperature, and the increase coefficient α of diffusion coefficient has a linear relationship with temperature. According to the mathematical expressions, the dehydrogenation process of TiMn1.5 alloy at different temperatures can be predicted. The research results can provide theoretical guidance for the safe, efficient and controllable application of hydrogen storage materials.

Design and optimization for a longitudinal-flow corn ear threshing device of low loss and low energy consumption

The traditional corn grain harvester threshing device has the problems of high grain breakage rate, high unthreshed grain rate and high energy consumption when harvesting high water content corn ears. A longitudinal-flow corn ear threshing device and its measurement and control system were proposed to overcome these problems. The working performance and energy consumption of the threshing device were optimized by conducting three factors and five levels corn ear threshing experiments. The experiments took the threshing cylinder speed (X1), threshing gap (X2), and guide vane angle (X3) as the experimental factors, and the grain breakage rate (Y1), unthreshed grain rate (Y2), unit energy consumption (Y3), and threshing concave pressure (Y4) as the experimental indicators. According to the experimental results, the quadratic polynomial regression models between experimental indicators and experimental factors were established. Through models optimization, the optimal working parameters for the threshing device were obtained as X1 at 392.40 r/min, X2 at 40.70 mm, and X3 at 33.16°. Through conducting verification experiment, it was found that under the optimal parameters, the experimental indicators were Y1 at 2.32 ± 0.06 %, Y2 at 0.48 ± 0.04 %, Y3 at 2.14 ± 0.10 kJ/kg, and Y4 at 46.28 ± 3.23N. The errors between the experimental results and the quadratic polynomial regression models were less than 5 %, which indicated that the models had high prediction accuracy. Compared with the unoptimized experimental indicators, the optimized experimental indicators Y1, Y2, Y3 and Y4 decreased by 36.26 %, 39.24 %, 14.74 % and 16.27 %, respectively. The working performance of the threshing device was significantly improved, and the energy consumption was significantly reduced. The relevant research could provide reference for the optimization of the mechanical structure and working parameters of the corn ear threshing device.

The effect of seasonal temperature difference on estimated wood density in Populus ussuriensis Kom. trees by the resistance drilling method

ABSTRACT Wood density is a main determinant of wood quality assessment for wood end-use and plantation trees. The resistance drilling method (RST) is one of the rapid assessment methods of wood density for standing trees. As the season changes, the water within trees occurs to freeze and is expected to indirectly affect RST results. However, the impact of ambient temperature is unknown. To investigate the effect of seasonal temperature difference on estimated wood density, the RST of Populus ussuriensis Kom. trees was examined across different seasons. A good linear regression model between average wood density and RST was established at normal temperature during summer, with a coefficient of determination of 0.708. The average RST of sapwood and heartwood increased by 6% to 22% from autumn (−5–0°C) to winter (−20–−10°C) compared to normal temperature in summer. Correspondingly, the average wood density estimated by RST increased by 4% to 16% from autumn to winter relative to normal temperature. The quadratic polynomial functions described the relationship between relative RST, relative wood density and seasonal temperature, with coefficients of determination over 0.922. Seasonal temperature had a significant effect on wood density, which was overestimated by RST in winter. This overestimation should be considered in the RST application.

Quadratic equations with absolute values: an example of developing proof in mathematics students

Proof is the most important and fundamental aspect of mathematics. However, it is generally agreed by mathematics teachers at upper high school and first year university that students lack the ideas of proof. How to develop this in students is a common, difficult and perennial problem. In this paper, we develop some ideas of proof based on the number of solutions of an equation involving a quadratic polynomial and absolute values of linear functions. We begin with the simple idea of making more precise a question that is posed, investigating the problem through exploration, and arriving at some conjectures. We proceed to determine ways to prove the conjectures and thus convert them into theorems. The question discussed in this paper arose in a session for high school students held at the Department of Mathematics and Statistics of the University of Western Australia. The result is an excellent and interesting illustration of problem posing and solving in mathematics that underpins mathematical thinking. The paper is accessible to final year high school and first-year university mathematics students. We expect that it will serve as a resource for and inspire further ideas and examples for mathematics teachers, for teaching proof to students.

Analysis of Optimal Water Levels in the Great Lakes Based on A Comprehensive Satisfaction Function

The purpose of this paper is to analyze the optimal water levels in the Great Lakes to meet the needs of multiple stakeholders and thus achieve sustainable development in the region. The Weight-Function-Synthesis-Optimization (WFSO) model was used in this study. By classifying the water level needs of different interest groups, their respective satisfaction functions are established, and the overall satisfaction function is formed by weighting. In addition, the quadratic polynomial function is used to fit the optimal monthly water level time series of Lake Ontario, and the fitting effect is good, fully reflecting the periodic and seasonal changes in the water level of Lake Ontario. By considering the priorities of various stakeholders, this paper defines an overall satisfaction metric, "allsa," and identifies a time series of monthly optimal water levels for Lake Ontario and beyond. The ideal water level was determined to be 74.9 meters. The study results suggest that maintaining this water level can maximize the satisfaction of ecosystems, transportation, real estate, terminals, and hydropower companies, and promote sustainable development of the region.

On possible limit functions on a Fatou component in non-autonomous iteration

Abstract The possibilities for limit functions on a Fatou component for the iteration of a single polynomial or rational function are well understood and quite restricted. In non-autonomous iteration, where one considers compositions of arbitrary polynomials with suitably bounded degrees and coefficients, one should observe a far greater range of behavior. We show this is indeed the case and we exhibit a bounded sequence of quadratic polynomials which has a bounded Fatou component on which one obtains as limit functions every member of the classical Schlicht family of normalized univalent functions on the unit disc. The proof is based on quasiconformal surgery and the use of high iterates of a quadratic polynomial with a Siegel disc which closely approximate the identity on compact subsets. Careful bookkeeping using the hyperbolic metric is required to control the errors in approximating the desired limit functions and ensure that these errors ultimately tend to zero.

Design and Experimental Optimization of an Automated Longline-Suspended Oyster Spat Insertion Device

To address the challenges of labor-intensive and costly manual oyster spat insertion in longline-suspended farming, an automated oyster spat insertion device was designed based on negative pressure suction and bundling fixation technologies. Using this device as the experimental platform, a three-factor, three-level Box–Behnken experiment was conducted, with fixation mechanism inclination, negative pressure suction cup span, and horizontal distance between turnover and fixation mechanisms as the experimental factors. The performance of the device was evaluated using the effective fixation rate and damage rate as the experimental indicators. The quadratic polynomial regression models were established to assess the impact of these factors on operational performance, while the response surface method was employed to analyze the interaction effects between factors. Parameter optimization and experimental validation were also performed. The results indicate that the factors affecting the effective fixation rate, in order of significance, are as follows: fixation mechanism inclination, horizontal distance between turnover and fixation mechanisms, and negative pressure suction cup span. For the damage rate, the order of significance is as follows: fixation mechanism inclination > negative pressure suction cup span < horizontal distance between turnover and fixation mechanisms. The optimization results show that when the fixation mechanism inclination is set at 43°, the negative pressure suction cup span at 27 mm, and the horizontal distance between turnover and fixation mechanisms at 179 mm, the effective fixation rate reaches 92.08%, and the damage rate is 4.71%. The relative errors between the measured and model-predicted values are less than 5%, indicating that the regression models are reliable. This research provides valuable insights for advancing the mechanization of the oyster farming industry and replacing manual labor with mechanized equipment.

Stability Analysis of Matrices and Single-Parameter Matrix Families on Special Regions

This paper proposes an efficient method for determining the D-stability of matrices using Kelley’s cutting-plane method. The study examines the D-stability of matrices in symmetric regions of the complex plane, defined by quadratic matrix inequalities (QMI) and polynomial functions. Using Kelley’s cutting-plane method, we present an iterative algorithm for determining the D-stability of a given matrix. Further, the robustness of single-parameter matrix families is analyzed, and a method is proposed for considering their D-stability. Through examples, we indicate the possible applicability of the proposed approach in addressing stability problems in linear systems.

Evaluation Indexes of Skid Resistance of Epoxy Chip Seal Based on Texture Features at Different Scales

Epoxy chip seals are widely used to improve the skid resistance of cement concrete pavements, which is significantly affected by surface texture. However, current methods for characterizing the surface texture structure are not precise, and the standard is not uniform. Therefore, a high-toughness modified epoxy resin chip seal structure was developed to conduct an indoor accelerated abrasion test. The elevation data of the epoxy chip seal under different abrasion times and different abrasion loads were obtained using laser scanning, and the density/sharpness combination parameters were obtained using the Hilbert–Huang transform and spectral analysis. The correlation between the texture parameters and the dynamic friction coefficient was analyzed using a stepwise multivariate quadratic polynomial method. The results showed that the texture structure of the epoxy chip seal surface is positively distributed, and the macroscopic texture occupies 49.45%, while the probability of the microscopic texture is only 4.55%. Meanwhile, the correlation coefficient between the texture parameters and the dynamic friction coefficient is 0.9307, which demonstrates that the selected texture parameters discard the texture components unrelated to skid resistance performance and reflect the distribution of the pavement texture and the skid resistance performance well.

Reliability analysis of support strategies in tunnel construction: Insights from geomechanical analysis of jointed rock masses

In this study, the dynamics of jointed rock masses in the challenging geological setting of the Himalayas, with a focus on tunneling activities and recommendations of support for jointing rock mass, were investigated. The jointing in Himalayan rocks mass poses significant implications for tunnel stability, demanding a detailed analysis of joint characteristics, such as joint connectivity and spacing. The parameter of joint connectivity rate along the Himalayas becomes a key focus, impacting rock mass strength for tunneling. The study utilized quadratic polynomial and reciprocal expressions of power functions, to characterize the nonlinear variation of jointed rock mass strength concerning joint connectivity rate. Integration of these results leads to unified equations that consider rock type dependence, having a realistic representation of jointed rock behavior. Numerical analysis reveals that jointing in rock affects instability through complex stress regimes, identifying critical stress concentration points. The effectiveness of support measures like rock bolts and shotcrete are validated, demonstrating their role in reducing displacements in tunnels.

Improving AGB estimations by integrating tree height and crown radius from multisource remote sensing.

Precise estimation of forest above ground biomass (AGB) is essential for assessing its ecological functions and determining forest carbon stocks. It is difficult to directly obtain diameter at breast height (DBH) based on remote sensing imagery. Therefore, it is crucial to accurately estimate the AGB with features extracted directly from RS. This paper demonstrates the feasibility of estimating AGB from crown radius (R) and tree height (H) features extracted from multi-source RS data. Accurate information on tree height (H), crown radius (R), and diameter at breast height (DBH) can be obtained through point clouds generated by airborne laser scanning (ALS) and terrestrial laser scanning (TLS), respectively. Nine allometric growth equations were used to fit coniferous forests (Larix principis-rupprechtii) and broadleaf forests (Fraxinus chinensis and Sophora japonica). The fitting performance of models constructed using only "H" or "R" was compared with that of models constructed using both combined. The results showed that the quadratic polynomial model constructed with "H+R" fitted the AGB estimation better in each vegetation type, especially in the scenario of mixed tall and short coniferous forests, in which the R2 and RMSE were 0.9282 and 25.30 kg (rRMSE 17.31%), respectively. Therefore, using high-resolution data to extract crown radius and tree height can achieve high-precision, global-scale estimation of forest above ground biomass.

Insights into the pore structure effect on the mass transfer of fuel cell catalyst layer via combining machine learning and multiphysics simulation

Analysis of the catalytic layer (CL) pore structure and three-phase (electron phase, proton phase, and reactant phase) mass transfer in high-temperature polymer electrolyte membrane fuel cell (HT-PEMFC) is critical for improving concentration polarization and optimizing performance. However, there is a lack of studies on the pore structure’s impact on the catalytic layer three-phase mass transfer. In this work, the influence of pore structure on catalytic layer three-phase mass transfer and multiphysics distribution was investigated by combining machine learning and multiphysics simulation. Among many key factors investigated by machine learning that impact the performance of catalytic layer, porosity emerges as the primary influencing factor. Porosity accounts for 32.7 % of the electric potential drop, with macro/micro porosity contributing 27.6 % and 5.1 %, and 32.8 % of the current density, with macro/micro porosity contributing 15.6 % and 17.2 %. Furthermore, the macropore structure has a much greater influence on the performance of the catalytic layer compared to the micropore structure. Moreover, the simulation results demonstrated that porosity has a great influence on three-phase mass transfer, the oxygen molarity increases with increasing porosity. The electric potential difference increases exponentially as porosity increases. The relationship between current density and porosity is a volcanic relationship, which can be expressed as a quadratic polynomial function. The mesoscopic pore-scale model (PSM) with an εeff of 0.502 (εmic of 0.2 and εmac of 0.378) exhibits the highest mean current density at 619.526 mA/cm2@0.5 V, attributed to a more uniform and efficient three-phase transfer path. The accuracy of the mesoscopic pore-scale model and the polynomial equation is further confirmed through corresponding experiments. The experiment results show that the current density decreased as the εeff increased from 0.682 to 0.702, which aligns with the theoretical predictions of the PSM model and polynomial equation. These studies are valuable for comprehending the internal three-phase mass transfer behavior and optimizing the catalytic layer pore structure to enhance HT-PEMFC performance.

Study of Fifth-Order Nonlinear Caudrey–Dodd–Gibbon Model for Multiwave, M-Shaped Solitons, Lumps, Generalized Breathers, Manifold Periodic, Rogue Wave and Kink Wave Interactions

Numerous novel wave structures, such as lump, lump with one-kink, lump with two-kink soliton, generalized breather, Ma breather, Kuznetsov-Ma breather, Akhmediev breather, manifold periodic, and rogue wave solutions to [Formula: see text]-dimensional fifth-order nonlinear Caudrey–Dodd–Gibbon (FNCDG) model via symbolic computation are studied based on the ansatz function scheme. Studying the lump-type solution involves selecting the function as the generic quadratic polynomial function. The lump with one- and two-kink solutions is created by mixing a quadratic function with one or two exponential functions. By adding hyperbolic function with a quadratic function, the rogue wave solutions are manipulated. In addition, the multiwave, [Formula: see text]-shaped rational solitons and their interactions with kink waves are analytically evaluated. Furthermore, different 3D, 2D, and contour profiles are created in different dimensions by changing the parameter values.

The Myth of the Decline Effect in Psi Research: The Empirical Evidence

The decline effect (DE) has been discussed in “psi” research since the early times of experimental investigations, and many causes have been advanced from: individual psychology, social attitudes, electromagnetic fields, experimental artifacts, or physical properties often related to quantum physics. Bierman (2001) found small and statistically significant decline slopes in all experimental protocols, but the mind-matter interaction with random number generators, where he found a positive quadratic polynomial slope. This study aimed to update Bierman’s results, taking into account all studies completed up to 2023 and analyzed in different meta-analyses. Five experimental protocols were analyzed: including anomalous perception in a Ganzfeld condition, remote viewing, forced-choice design in extra-sensory perception, predictive physiological anticipation, and dream extra-sensory perception studies. The results showed that only one slope coefficient out of the five examined was statistically significant, indicating that there was no evidence of a general DE across the different experimental protocols.

Durability Investigation of Ultra-Thin Polyurethane Wearing Course for Asphalt Pavement

In this study, a wear-resistant ultra-thin wear layer was fabricated with polyurethane as an adhesive to investigate its durability for pavement applications. Its road performance was investigated based on indoor tests. First, the abrasion test was performed using a tire–pavement dynamic friction analyzer (TDFA), and the surface elevation information of the wear layer was obtained by laser profile scanning. The relationship between the anti-skid properties of the wear layer and the macro-texture was analyzed. Second, a Fourier infrared spectrometer and scanning electron microscope were employed to analyze the evolution of polyurethane aging properties in the pull-out test and accelerated ultraviolet (UV) aging test. The results showed that the mean profile depth (MPD), arithmetic mean wavelength of contour (λa), surface wear index (SBI), stage mass loss rate (σ), and total stage mass loss rate (ω) of the abrasive layer aggregate had significant multivariate quadratic polynomial relationships with the skidding performance of the abrasive layer. The tensile strength of the polyurethane ultra-thin abrasive layer decreased by only 2.59% after 16 days of UV aging, indicating a minimal effect of UV action on the aggregate and structural spalling of the polyurethane abrasive layer.

Capacity analysis of short-distance continuous diversion areas on mountainous urban expressways.

The short-distance continuous diversion area plays a crucial role within mountainous urban expressway systems, significantly enhancing the efficiency of specialized road sections through capacity analysis. This study develops a capacity calculation model tailored to the diversion area's unique characteristics and principal capacity-influencing factors. Initially, the research focuses on a specific short-distance continuous diversion area of a mountainous urban expressway, employing video trajectory tracking technology to gather trajectory data. This data serves as the basis for analyzing road and traffic characteristics. Subsequently, the model computes the capacity influenced by eight variables, including diversion point spacing and deceleration lane length, using VISSIM simulation experiments. A gray correlation analysis identifies key factors, which guide the establishment of the model's fundamental structure through two-factor surface fitting results. Mathematical statistical methods are then applied to resolve the model's parameters, culminating in a robust capacity calculation model. The findings reveal that diversion point spacing, along with primary and secondary diversion ratios, significantly influence capacity. Notably, the capacity exhibits a marked quadratic polynomial relationship with the primary diversion ratio and diversion point spacing, and a linear relationship with the secondary diversion ratio. The model's validity is confirmed through a case study at the diversion area north of Huacun Interchange in Chongqing Municipality, where the discrepancy between calculated and actual capacities is under 5%, underscoring the model's high accuracy. These results offer valuable theoretical and methodological support for the planning, design, and traffic management of diversion areas.