Polynomial Function Research Articles

Assessment of Digital Image Correlation Effectiveness and Quality in Determination of Surface Strains of Hybrid Steel/Composite Structures.

The application of the digital image correlation (DIC) contactless method has extended the possibilities of reliable assessment of structure strain fields and deformations throughout the last years. However, certain weak points in the analyses using the DIC method still exist. The fluctuations of the results caused by different factors as well as certain deficiencies in the evaluation of DIC accuracy in applications for hybrid steel/composite structures with adhesive joints are one of them. In the proposed paper, the assessment of DIC accuracy based on the range of strain fluctuation is proposed. This relies on the use of a polynomial approximation imposed on the results obtained from the DIC method. Such a proposal has been used for a certain correction of the DIC solution and has been verified by the introduction of different error measures. The evaluation of DIC possibilities and accuracy are presented on the examples of the static tensile tests of adhesively bonded steel/composite joints with three different adhesives applied. The obtained results clearly show that in a non-disturbed area, very good agreement between approximated DIC and FEM results is achieved. The relative average errors in an area, determined by comparison of DIC and FEM strains, are below 15%. It is also observed that the use of approximated strains by polynomial function leads to a more accurate solution with respect to FEM results. It is concluded that DIC can be successfully applied for the analyses of hybrid steel/adhesive/composite samples, such as determination of strain fields, non-contact visual detection of faults of manufacturing and their development and influence on the whole structure behavior during the strength tests, including the elastic response of materials.

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics

The transport of heat in an unsteady flow of nanofluid has been discussed in this paper. The flow is maintained over a non-flat, variably porous, and moving sheet in the present simulation. Moreover, the sheet has both constant temperature and nanoparticle concentration at its surface. Unsteadiness in all field variables (i.e. the flow, temperature, and nanoparticles concentration) has been produced by the time-dependent quantities, specified at the surface of the sheet (i.e. kinematics of sheet). The well-known Buongiorno model of nanofluid has been undertaken in the present studies. Furthermore, the simulation includes the particular cases of uniform and linear (polynomial & algebraic functions) stretching/shrinking and injection/suction velocities. Besides that observations of the same nature have been recorded for the non-flat sheet. The boundary layer form of the governing PDEs has been utilized to evaluate the exact status of field variables in the flow domain. Appropriate conditions are imposed by considering the geometry of the flow problem. The problem at hand is simplified by introducing a new set of functions for the field variables because of boundary inputs. After this treatment, the system of boundary value ODEs, which contains several dimensionless numbers (parameters), has appeared, and the problem is solved numerically for various values of parameters, involved in it. More precisely, effects of unsteadiness, wall roughness, surface deformation parameters, Prandtl, Schmidt, thermophoretic, and Brownian motion numbers have been seen on profiles of four field variables. Besides that, the numerical results are also obtained for the skin friction coefficient, Nusselt, and Sherwood numbers. The present modelled problem and its solution are compared with classical models of that particular nature and with their solutions.

Cattle manure thermochemical conversion to hydrogen-rich syngas, through pyrolysis and gasification

The fundamental significance of using cattle manure as a case study is the risk of continuing pollution, caused by its poor management in connection to the increasing demand for animal-derived food. Pyrolysis and gasification, effective solutions with real valorization potential, are the proposed techniques of converting this type of waste into valuable products. After a complete initial characterization, cattle manure is converted into hydrogen-rich syngas, using a modular hybrid fixed-bed reactor, at a generous thermal range, 700 °C to 875 °C, under different process agents, without the use of steam or the addition of catalysts. In comparison to gasification, the quantification of syngas demonstrates higher yields in pyrolysis processes, but with a lower energy potential. The content of the syngas in hydrogen, ⁓ 25 vol% and hydrocarbons, ⁓ 25 vol%, emphasized by an energetic value of ⁓ 17 MJ/m3, holistically places the gasification process in a slight advantage in relation to pyrolysis, exceeding the values presented by other studies on similar matrices and technical conditions. The forecast investigation of syngas composition through polynomial functions shows a significant drop in hydrogen and hydrocarbon concentrations after the 80-min sampling period.

Tidal and residual currents in the inner shelf of East China Sea detected from underway ADCP observations

Characterizing the spatial variability of net flow transport in a tide-dominated area like the East China Sea (ECS) is key to understanding the material and heat budget as well as their impacts on local ecosystem. However, the residual circulation in the ECS was much less confirmed by observations as it can only be derived from very sparse mooring data. Here for the first time we obtain the spatial patterns of tidal and residual currents in the inner ECS shelf from ADCP underway measurements conducted in 12 cruises using a spatial least squares (SLS) fitting technique. The SLS method is validated with the traditional harmonic analysis using numerical simulation results and then implemented with the observational data. The tidal current is dominated by two semidiurnal components M2 and S2 in this area, with the major axis of tidal ellipse along northwest-southeast direction. The ADCP-derived tide parameters are in good agreement with those from the mooring data and barotropic tide model. The annual spatial pattern of residual circulation is characterized by a southward coastal current and a northward shelf current, which are identified as the East China Sea Coastal Current (ECSCC) from Changjiang River runoff and the Taiwan Warm Current (TWC) originated from Taiwan Strait and Kuroshio. Their magnitudes are comparable but of one order smaller than tides. The vertical structure of TWC shows a subsurface-intensified feature in line with previous mooring observations. The north limit of TWC is approximately at 31.5°N around the submerged valley, beyond which the northward TWC becomes almost invisible. By a series of virtual cruise experiments, we show that the observation data length is the most crucial factor controlling the SLS fitting accuracy, while the role of other factors like sampling frequency is secondary. With a fixed-length dataset, the degree of polynomial function used for SLS fitting must be properly determined to minimize the under-fitting and over-fitting error, and there is also a trade-off in the fitting accuracy between tidal and residual currents depending on the fitting strategy.

Computational modelling and prediction of nonlinear deflection responses of bonded joint component with multiple damage (crack and delamination) – An experimental validation

The present research evaluates the presence of damage, including delamination and cracks, affects the deflection response of an adhesively bonded single lap joint (SLJ). In this study, the numerical analysis is performed for intact and influence of different damages in the adherend of SLJ in the commercial simulation software (ABAQUS). The circular delamination of radius ‘R’ 10 mm and crack having length ‘l’ 20 mm, the radius of curvature ‘Rc’ 0.2 mm are imposed into the laminate adherend using node-to-surface interaction technique. The stability of the simulation model is verified by comparing the deflection values from published results and experimental data. The confirmed simulation model is broadened to examine the impact of design factors (fiber orientation, loading position, delamination shape, crack position and orientation, and delamination position with and without crack) on the deflection response for various overlapping lengths (25, 30, 35, and 40 mm) for final design recommendation. Additionally, the sensitivity analysis was performed using a surrogate model (i.e., variance-based method) by constructing the second-order polynomial function to quantify the influence of damages under the input parameters. The detailed features and multivariate model functions have been analysed for the various damage cases of SLJ.

Influence of control parameters on the stabilization of an Euler-Bernoulli flexible beam

In this work, we numerically study the influence of control parameters on the stabilization of a flexible Euler-Bernoulli beam fixed at one end and subjected at the other end to a force control and a punctual moment control proportional respectively to velocity and rotation velocity. First, we analyze the displacement stabilization and the asymptotic behavior of the beam energy using a stable numerical scheme, resulting from the Crank-Nicholson algorithm for time discretization and the finite element method based on the approximation by Hermite's cubic polynomial functions, for discretization in space. Then, by means of the finite element method, we represent the spectrum of the operator associated with this beam problem and we carry out a qualitative study of thelocus of the eigenvalues according to the positive control parameters. From these studies we conclude that rotation velocity control has more effect on the stabilization of the beam compared to velocity control. Finally, this result is confirmed by a sensitivity study on the control parameters involved in the stabilization of the beam.

Prediction Model of Spontaneous Combustion of Lignite in Zhalainuoer Mining Area.

A programmed temperature-increase experiment was conducted on coal samples from four coal mines in the Zhalainuoer mining area to improve the accuracy of predicting and forecasting lignite spontaneous combustion. The gases produced during the coal tests were analyzed, and logistic, exponential, Boltzmann, and fourth-degree polynomial functions were selected to develop predictive models for the gas data. Additionally, the Boltzmann function was used to predict the occurrence of fire. The results revealed that the initial appearance temperature of CO was approximately 50 °C, and it exhibited an exponential growth trend with increasing temperature. The initial appearance temperature of C2H4 was approximately 140 °C, which could serve as an indicator of coal entering the accelerated oxidation stage. Applying the selection principle to gas indicators, CO and C2H4 were identified as single gas indicators for lignite spontaneous combustion in the Zhalainuoer mining area, whereas CO/CO2 and C2H4/C2H6 were identified as composite gas indicators. Among the four functions, the Boltzmann function model exhibited the best fitting effect for CO and CO/CO2 within the temperature range of 0-200 °C. The values of the four parameters (A 1, A 2, dx, and x 0) were determined based on their statistical characteristics, and a functional equation describing the relationship between gas concentration and coal temperature was derived. This indicates that the Boltzmann function model can be effectively used to predict the spontaneous combustion of lignite in the Zhalainuoer mining area.

Scalar's quasibound states in cosmological black hole background

In this letter, we present in detail a novel exact solution of scalar quasibound states of a static spherically symmetric Schwarzschild de Sitter black hole. We investigate and work out the governing covariant scalar field wave equation, i.e., the Klein-Gordon equation and isolate the radial equation. In this letter, we show in detail, the derivation of the successfully obtained exact radial wave solutions which are expressed in terms of General Heun functions. Having the exact solutions in hand, the energy levels expression is obtained from special function's polynomial condition. In the last part, the Hawking radiation is investigated via the Damour-Ruffini method and the Hawking temperature is obtained from radiation distribution function.

An Investigation of Molecular Property Prediction and Classification Based on Machine Learning Algorithms

With the rapid advancement of science and technology, chemical and physical research has entered an era of complexity and high dimensionality, where traditional research paradigms struggle to optimize vast chemical parameter searches. The Machine Chemist platform was developed in this context, leveraging big data and intelligent models to automate chemical synthesis, characterization, and testing processes. This study aims to predict the y1, y2 and y3 properties and classes of 2,580 molecules based on their physicochemical properties and improve model accuracy through data analysis and modeling. Data preprocessing involved removing missing values, duplicates, and outliers using the quartile method, resulting in an analyzable dataset. A scatter plot of y2 and id suggested a univariate polynomial function relationship, leading to the construction of a univariate nonlinear regression model. The model achieved a high prediction accuracy, with a low root mean square error and a high coefficient of determination. Additionally, the relationship between class and y1~y3 , x1~x100 indicators was examined, revealing mostly nonlinear relationships. A random forest model was established to classify 2,580 molecules into 1 to 4 classes based on the properties of 200,000 chemical molecules. The model's performance was evaluated using decision trees, confusion matrices, precision, and recall metrics. Finally, the SHAP method assessed the impact of feature indicators on classification outcomes, contributing to the development of a reliable molecular category prediction model.

Modeling Human Macular Cone Photoreceptor Spatial Distribution.

The purpose of this study was to investigate the spatial distribution of human cone photoreceptors and examine cone density differences between the retinal meridians and quadrants. Using adaptive optics scanning laser ophthalmoscopy, the maculae were imaged in 17 eyes of 11 subjects with normal chorioretinal health aged 54 to 72 years. We measured cone density at 325 points within the central 10degrees radius of the retina. Cone density spatial distributions along the primary retinal meridians and in four macular quadrants (superior-nasal, superior-temporal, inferior-temporal, and inferior-nasal) were analytically modeled using the polynomial function to assess the meridional and quadrantal difference. The mean and 95% confidence interval for the prediction of cone density along the primary retinal meridians was modeled with a 7-degree one-variable polynomial (R2 = 0.9761, root mean squared error [RMSE] = 0.0585). In the 4 retinal quadrants, cone density distribution was described by a 2-variable polynomial with X degree 3 and Y degree 4 (R² = 0.9834, RMSE = 0.0377). The models suggest no statistically significant difference between medians and between quadrants. However, cone density difference at corresponding spatial locations in different areas can be up to 25.6%. The superior-nasal region has more areas with high cone density, followed by quadrants of inferior-nasal, inferior-temporal, and superior-temporal. Analytical modeling provides comprehensive knowledge of cone distribution across the entire macula. Although modeling analysis suggests no statistically significant difference between medians and between quadrants, the remarkable cone density discrepancies in certain regions should be accounted for in applications requiring sensitive detection of cone variation.

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ, provided that a sample set (of size N) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N=mO(1ɛ), was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n, with N=poly(ɛ−1,n,ln1δ), where poly denotes a polynomial function, and (1−δ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N=poly(ɛ−1,lnnδ). Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

Моделювання інжекції газу в надзвукову частину сопла при газодинамічному регу-люванні вектора тяги

Solid-propellant rocket engines are simple in design, highly reliable, and able to store the propellant for a long time without its degradation. Their main feature is that the propellant is a mixture of a solid fuel and a solid oxidizer, thus ensuring a uniform combustion and a stable discharge of the combustion products. However, the combustion rate cannot be controlled, and the combustion cannot be stopped or restarted. This calls for efficient methods of thrust vector control. Gas-dynamic methods, such as a gas injection into the supersonic nozzle area, offer a required flight path control without complex high-power mechanical systems. The importance of this study lies in improving the accuracy and efficiency of rocket flight control, which is critical for today’s space and defense tasks. The numerical simulation of gas-dynamic control systems, in particular by an asymmetric gas injection, allows one to obtain detailed data on the flow behavior and optimize the design and operating conditions of the system. This study is concerned with a full-scale solid-propellant rocket engine with a gas-dynamic thrust vector control system based on the use of asymmetric forces that occur on the nozzle wall when the supersonic flow interacts with the injected transverse jets. To simulate the process in the Ansys Fluent software package, a geometric model of a nozzle with an asymmetric injection of the chamber gas into the supersonic area was developed. The injection flow rate was controlled by moving the valve flap. The simulation was carried out taking into account the temperature dependence of the main thermophysical gas parameters with consideration for dissociation processes by way of data approximation. The approximation was performed using piecewise polynomial functions. Nozzle flow patterns were obtained. The calculated results were compared with experimental test data and shown to be in satisfactory agreement with the lateral force measured during the fire bench tests of the prototype. From a practical point of view, the results obtained may be directly used to improve existing thrust vector control systems and develop new ones. This will improve rocket navigation accuracy, flight stability, and maneuverability, which is critical for complex space and defense tasks.

E-PINN: extended physics informed neural network for the forward and inverse problems of high-order nonlinear integro-differential equations

Physics informed neural network (PINN) is a new deep learning paradigm, which embeds the physical information delineated by PDEs in the loss function and optimizes the weights in the neural network. Based on PINN, an extended PINN(E-PINN) is proposed, which is a mixture of the polynomial function approximation method and PINN's learning framework. A preprocess layer is added before the classical PINN, using Legendre polynomials as the polynomial basis function. Therefore, E-PINN not only has the excellent approximation ability of the polynomial basis function, but also inherits the learning framework of the neural network method. In numerical experiments, the proposed E-PINN algorithms have high accuracy in solving 1D, 2D high-order nonlinear Fredholm equations and equations system, including the forward and inverse problems.

An Update to The Demagnetizing Factor Dataset Calculated for The General Ellipsoid by Osborn

The exact formulae for calculating the demagnetizing factors of a general ellipsoid along the three main axes a ≥ b ≥ c have been long known. According to these formulae, the demagnetizing factors depend only on the axial ratios b/a and c/a. Although the calculation of the demagnetizing factors is a straightforward task, the calculation itself is not a simple one. Therefore, tabular and graphical representations of these demagnetizing factor data have also been presented which can then be used for approximating the demagnetizing factors of a rectangular ferromagnetic slab with the same axial ratios. It turned out in our recent study, however, that, in some ranges of axial ratios (e.g., for very small c/a values), the available tables and graphs do not provide sufficient resolution for obtaining the demagnetizing factors with reasonable accuracy. It was decided to calculate these missing values, and they are presented here in both tabular and graphical form by giving instructions for how to obtain conveniently further interpolated data. In addition, the previous and current demagnetizing factor data have been replotted and fitted to a polynomial function with high accuracy. The functional form of these fitting polynomials is presented in a table for the whole range of the axial ratios b/a and c/a. By graphically displaying these functions, one can obtain, in a relatively simple manner, the demagnetizing factors of a general ellipsoid with known axial ratios without the need to directly calculate through the exact formulae. This may be helpful in obtaining a quick estimate for the demagnetizing factors of any rectangular ferromagnetic slab of interest.

The importance of global synchronous observation for estimating oceanic chlorophyll-a

Over the last three decades, ocean color satellites have recorded continuous change in phytoplankton concentration, and in doing so, the satellites have helped marine remote sensing to become an emerging discipline. However, ocean color satellite has provided the state of global phytoplankton only around midday whereas phytoplankton have significant diurnal variation characteristics over an entire day-night cycle, which would lead to large estimation uncertainty in downstream products. A large global field observations show that the diurnal variation curves can be constructed as the sum of an exponential and a polynomial function. After correction with our diurnal variation curves, the intermission difference between MODISA and MODIST phytoplankton product could be decreased from 7.57% to 6%, which is critical to monitor the long-term changing trend with multi-mission data. When the satellite-recorded chlorophyll-a concentration is simply equal to a daily average value, it results in overestimating uncertainties of 16% and 54% for the northern and southern hemispheric oceans, respectively. Moreover, as a typical example of downstream product of the chlorophyll-a, the coverage of oligotrophic waters can oscillate 76% from day to night simulated from satellite images with our diurnal variation curves, further confirming the importance of global synchronous observation. The geostationary satellite might be an efficient regional tool for diurnal observation, but it must account for its limitations under the weak light conditions of early morning and late afternoon. In the real world, the effects of diurnal variations in ocean properties reach far beyond chlorophyll-a in the global oceans. We anticipate these quantitatively findings to be a starting point for quantitatively re-examining the proper application of ocean color products in scientific communication.

A fifth order block methods for solving second-order stiff ordinary differential equations using trigonometric functions and polynomial function as the basis function

A fifth order block methods for solving second-order stiff ordinary differential equations using trigonometric functions and polynomial function as the basis function

Superdiffusive planar random walks with polynomial space–time drifts

We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of the present time. We describe how the model was motivated through an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent 3/4. The self-interacting process originated in discussions with Francis Comets.

Application of artificial intelligence in modeling of nitrate removal process using zero-valent iron nanoparticles-loaded carboxymethyl cellulose.

This study explores nitrate reduction in aqueous solutions using carboxymethyl cellulose loaded with zero-valent iron nanoparticles (Fe0-CMC). The structures of this nano-composite were characterized using various techniques. Based on the characterization results, the specific surface area of Fe0-CMC measured by the Brunauer-Emmett-Teller analysis were 39.6m2/g. In addition, Scanning Electron Microscopy images displayed that spherical nano zero-valent iron particles (nZVI) with an average particle diameter of 80nm are surrounded by carboxymethyl cellulose and no noticeable aggregates were detected. Batch experiments assessed Fe0-CMC's effectiveness in nitrate removal under diverse conditions including different adsorbent dosages (Cs, 2-10mg/L), contact time (t, 10-1440min), initial pH (pHi, 2-10), temperature (T, 10-55°C), and initial concentration of nitrate (C0, 10-500mg/L). Results indicated decreased removal with higher initial pHi and C0, while increased Cs and T enhanced removal. The study of nitrate removal mechanism by Fe0-CMC revealed that the redox reaction between immobilized nZVI on the CMC surface and nitrate ions was responsible for nitrate removal, and the main product of this reaction was ammonium, which was subsequently completely removed by the synthesized nanocomposite. In addition, a stable deviation quantum particle swarm optimization algorithm (SD-QPSO) and a least square error method were employed to train the ANFIS parameters. To demonstrate model performance, a quadratic polynomial function was proposed to display the performance of the SD-QPSO algorithm in which the constant parameters were optimized through the SD-QPSO algorithm. Sensitivity analysis was conducted on the proposed quadratic polynomial function by adding a constant deviation and removing each input using two different strategies. According to the sensitivity analysis, the predicted removal efficiency was most sensitive to changes in pHi, followed by Cs, T, C0, and t. The obtained results underscore the potential of the ANFIS model (R2 = 0.99803, RMSE = 0.9888), and polynomial function (R2 = 0.998256, RMSE = 1.7532) as accurate and efficient alternatives to time-consuming laboratory measurements for assessing nitrate removal efficiency. These models can offer rapid insights and predictions regarding the impact of various factors on the process, saving both time and resources.

Genetic Selection Approach for Semen Characteristics in Thai Native Grandparent Roosters (Pradu Hang Dum) Using Random Regression Test-Day Models and Selection Indices.

The aim of this study was to analyze suitable genetic models and selection indices to estimate the genetic parameters and breeding values of native Thai roosters. A total of 3475 records of seven semen traits (mass movement, semen pH, semen color, volume, sperm viability, sperm abnormalities, and sperm concentration) from 242 Thai native grandparent roosters were analyzed. Multiple-trait random regression test-day models with five covariance functions were used to analyze the variance components, genetic parameters, and breeding values. The selection index (SI) was calculated to determine the optimal genetic value for different selection percentages. The results showed that a multiple-trait random regression test-day model with a second-order Legendre polynomial function was the most appropriate genetic model for this population. The estimated heritability values were low to moderate, ranging from 0.110 to 0.112 (mass movement), 0.040 to 0.051 (semen pH), 0.092 to 0.097 (semen color), 0.220 to 0.225 (semen volume), 0.067 to 0.083 (sperm viability), 0.086 to 0.099 (sperm abnormalities), and 0.134 to 0.138 (sperm concentration). The repeatability values exceeded the heritability values and were within the range of 0.133 to 0.688. The genetic correlations among semen traits ranged from -0.332 to 0.677, and phenotypic correlations ranged from -0.260 to 0.460. When considering heritability and genetic correlation values, semen volume, sperm concentration, and mass movement were the top three priority semen traits calculated as selection indices. Finally, the top 10% of the selection index was recommended for creating the next generation. Our findings provide useful information on genetic parameters and an appropriate selection index of semen traits for selecting the genetics of individual Thai native grandparent roosters. The heritability estimates for semen traits reported here suggest an adequate response to selection through a genetic evaluation approach. Our results indicate that it is possible to select grandparent roosters with better reproductive performance.

A general quadratic enrichment of the Crouzeix–Raviart finite element

The Crouzeix–Raviart finite element method is widely recognized in the field of finite element analysis due to its nonconforming nature. The main goal of this paper is to present a general strategy for enhancing the Crouzeix–Raviart finite element using quadratic polynomial functions and three additional general degrees of freedom. To achieve this, we present a characterization result on the enriched degrees of freedom, enabling to define a new enriched finite element. This general approach is employed to introduce two distinct admissible families of enriched degrees of freedom. Numerical results demonstrate an enhancement in the accuracy of the proposed method when compared to the standard Crouzeix–Raviart finite element, confirming the effectiveness of the proposed enrichment strategy.