Power Polynomial Research Articles

ALGORITHM FOR CALCULATING SURFACES OF BIFOCAL LENS ANTENNAS

An algorithm is proposed that makes it possible to calculate the coefficients of power polynomials approximating the illuminated and shadow surfaces of bifocal lens antennas. The algorithm is based on providing equality of electrical lengths of rays passing from the focus points through lens body and its edge and on the assumption that the phase front is flat and is inclined at a determined angle relative to the main optical axis of the lens on the aperture of the lens antenna. For each of the rays an expression was written that determines its electrical length. The electrical length of the rays depends on the points coordinates of the illuminated and shadow surface of the lens, in which they are refracted. The analytical solution of the obtained equation is difficult. Therefore, it is proposed to determine the exact coordinate values by numerical methods. The proposed algorithm determines in series the three points lying on the illuminated and shadow surfaces. The coordinates of the points are used to form systems of equations whose solutions are the coefficients of power polynomials approximating the illuminated and shadow surfaces of the lens antenna. The algorithm does not impose restrictions on the relative dielectric constant of the material from which the lens antenna is made.

РОЗРОБКА СПОСОБУ ТА ЗАСОБУ ВИМІРЮВАНЬ НАПРУЖЕНО – ДЕФОРМОВАНОГО СТАНУ ЗА ДОПОМОГОЮ ТЕНЗОДАТЧИКА

Nowadays due to the modern wave of intellectualization of measuring instruments the digital methods of correction not only for primary measuring transducers, but also for secondary sensors are practiced on a large scale. Since the conversion function of secondary measuring transducers is linear, the method of model measures by two points is used for automatic correction of systematic components of the errors of such converters. The method of digital compensation, which provides a more significant reduction in the errors of measuring transducers compared with the method of analog compensation has been described. Features and technical indicators of this method are considered on the example of measuring pressure transducer with foil strain gauges. This method is universal, allows to adjust not only the errors of measurement channel nonlinearity and additional errors, but also the errors associated with the effect of interferences of general type due to ground resistance, which induces the connection between measuring channels of the main and destabilizing factor. The disadvantages of this method include a significant amount of computations, which sharply increases with the increase of the order of approximating polynomials. The aim of the paper is to develop a method and means of measuring stress-strain state using strain gauge, free from the above mentioned shortcomings. The main destabilizing factors that limit the measurement accuracy using strain gauge are the following: - random processes (noises, obstacles, etc.); - changes in parameters of measuring transducers due to aging and physical degradation; - effects of external climatic and mechanical factors (temperature, humidity, etc.). Regarding systematic components, the errors of nonlinearity and temperature component of the error are the most important in statistical measurements. We have studied the influence of temperature range variations, the spread of values of temperature error (± 10 %) on the mean square error of approximation by power polynomials. Using the NUMERY Program, the dependence of approximation error on the order of approximating polynomial has been determined. It is established that in a wide temperature range, the error for constantan has a weak relation with the order of a polynomial.

Free-carrier-driven Kerr frequency comb in optical microcavities: Steady state, bistability, self-pulsation, and modulation instability

Continuous-wave pumped optical microresonators have been vastly exploited to generate a frequency comb (FC) utilizing the Kerr nonlinearity. Most of the nonlinear materials used to build photonic platforms exhibit nonlinear losses such as multiphoton absorption, free-carrier absorption, and free-carrier dispersion which can strongly affect their nonlinear performances. In this work, we model the Kerr FC based on a modified Lugiato-Lefever equation (LLE) along with the rate equation and develop analytical formulations to make a quick estimation of the steady state, bistability, self-pulsation, and modulation instability (MI) gain and bandwidth in the presence of nonlinear losses. The analytical model is valid over a broad wavelength range as it includes the effects of all nonlinear losses. Higher-order $(g3)$ characteristic polynomials of intracavity power describing the steady-state homogeneous solution of the modified LLE are discussed in detail. We derive the generalized analytical expressions for the threshold (normalized) pump detuning that initiates the optical bistability when nonlinear losses are present. Free-carrier dispersion-led nonlinear cavity detuning is observed through the reverse Kerr tilt of the resonant peaks. We further deduce the expressions of the threshold pump intensity and the range of possible cavity detuning for the initiation of the MI considering the presence of nonlinear losses. The proposed model will be helpful in explaining several numerical and experimental results which have been previously reported and thereby will be able to provide a better understanding of the comb dynamics.

Application of Multidimensional Linearization in Quasi-Optimal Controllers Synthesis in the Functional of Generalized Work

The paper investigates the task of the analytically design of an optimal controllers (ADOC) as defined by A. A. Krasovskij for stable multidimensional objects, which are described by matrix differential equations with polynomial non-linearity from phase coordinates. The investigated class of polynomial control objects has a wide application: these models are used to describe the motion of systems with a very different nature — electromechanical equipment, chemical reactors, industrial recycling facilities, biological and ecological systems, etc. The most suitable task solution for the ADOC is the power series method, which in comparison with other methods, allows to finding control laws in widest range of the object’s phase space. However, its realization is dealt with a large amount of calculations and it is less formalized, so it comparatively hard for programming. In this paper the quasi-optimal controller’s synthesis method is suggested. It can reduce the disadvantages of the previously mentioned power series method. It uses the multidimensional linearization of polynomial objects procedure which implements extension of the object state space with new coordinates. These coordinates are the products of the original phase coordinates and the application of the matrix theory with the Kronecker product. The synthesis method can help to find an approximate ADOC task solution with a high degree of accuracy. The method is very easy to use, because it mainly based on uses of well-known software for the linear quadratic task solution in the optimal control. The ADOC task solution accuracy is defined by the accuracy of the corresponding degree (k = 2, 3...) that chosen for the object of the quasi-linearized model under study. It must be noted, that the k th power polynomial components of the control objects described, is considered in the k th power linearized model. Therefore, suggested synthesis method provides an accurate solution as a common power series method, holding its terms to the k th power inclusive. However, the devised synthesis method as a rule gives more accurate results, because it takes into account the functional matrix of the used quasilinear model of the object state augmented vector containing the original object’s phase coordinates products.

Inverse limits of Macaulay's inverse systems

Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay's inverse systems for Cohen–Macaulay factor algebras of formal power series or polynomial rings over an infinite field. On the way we find a strictness result for filtrations defined by regular sequences. It generalizes both a lemma of Uli Walther and the Rees isomorphism.

模拟降雨下麻栎林地表径流和壤中流及氮素流失特征

PDF HTML阅读 XML下载 导出引用 引用提醒 模拟降雨下麻栎林地表径流和壤中流及氮素流失特征 DOI: 10.5846/stxb201802040296 作者: 作者单位: 山东农业大学林学院,山东农业大学林学院,山东农业大学林学院,山东农业大学林学院,山东农业大学林学院,山东农业大学林学院 作者简介: 通讯作者: 中图分类号: 基金项目: 山东省自然科学基金项目（ZR2016CM49）；国家林业公益性行业专项课题（2014303-08） Characteristics of surface flow and interflow and nitrogen loss in Quercus acutissima forest land under simulated rainfall Author: Affiliation: Forestry College of Shandong Agricultural University,Forestry College of Shandong Agricultural University,Forestry College of Shandong Agricultural University,Forestry College of Shandong Agricultural University,Forestry College of Shandong Agricultural University,Forestry College of Shandong Agricultural University Fund Project: The Natural Science Foundation of Shandong Province,China(Grant No. ZR2016CM49); The Special Fund for Forestry Scientific Research in the Public Interest (No. 201404303-08) 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:为探讨人工林地地表径流和壤中流产流机制及其氮素流失规律，选择鲁中南山区典型林地麻栎林为研究对象，采用模拟降雨试验方法，研究麻栎林与荒草地的产流及氮素流失特征。结果表明：（1）麻栎林的总产流量、地表径流量、壤中流量分别是荒草地的80.5%、61.4%、162.2%。地表径流产流呈不断增加且趋于稳定的特征；壤中流产流时间明显滞后于地表径流的，产流过程径流量波动比较小，保持相对稳定。地表径流量和壤中流量随时间的变化过程可分别通过对数函数和多项式函数进行模拟。（2）麻栎林的全氮总流失浓度、地表径流全氮流失浓度、壤中流全氮流失浓度为11.5、13.1、8.9 mg/L，分别比荒草地低19.0%、13.8%、8.2%。地表径流全氮流失浓度一般前期较大，而后递减并趋于稳定；壤中流全氮流失浓度在整个产流过程中保持相对稳定。地表径流和壤中流全氮流失浓度随降雨时间的变化过程可分别通过幂函数和多项式函数进行模拟。（3）在整个降雨产流过程中，麻栎林和荒草地的地表径流量分别占总产流量的61.8%和81.1%，麻栎林和荒草地的地表径流全氮流失量分别占全氮总流失量的70.4%和87.0%，径流、氮素的流失都以地表径流为主。与荒草地相比，麻栎林具有明显增加壤中流，减少氮素流失效果。 Abstract:To explore the mechanism of runoff and loss of nitrogen in artificial forest surface flow and interflow, the typical Quercus acutissima forest in a hilly area of middle southern Shandong Province was evaluated as the research object. Simulated artificial rainfall experiments were carried out to examine the characteristics of runoff and nitrogen loss in Q. acutissima forest land and grassland. The results showed the following: (1) The total flow, surface flow, and interflow in the Q. acutissima forest land were 80.5%, 61.4%, and 162.2% of that in grassland, respectively. The surface flow process tended to increase and then were stable. The interflow generation time clearly lagged behind the surface flow, and the runoff fluctuation of interflow was relatively smaller and more stable than that of surface flow. The relationship between the logarithm function and polynomial function was determined from the surface flow and interflow and rainfall time. (2) The total nitrogen output density, total nitrogen output density of surface flow, and total nitrogen output density of interflow in the Q. acutissima forest land were 11.5, 13.1, and 8.9 mg/L, which were 19.0%, 13.8%, and 8.2% lower than those of grassland, respectively. The output density of nitrogen through surface flow was high at the initial time but was generally stable as simulated rainfall continued. The output density of nitrogen through interflow remained relatively stable throughout the runoff process. The concentration of runoff and total nitrogen loss in surface flow and interflow revealed a relationship between the power function and polynomial function. (3) Throughout the simulated rainfall process, the surface flow in Q. acutissima forest land and grassland accounted for 61.8% and 81.1% of the total runoff, respectively. Total nitrogen loss from the surface flow in Q. acutissima forest land and grassland accounted for 70.4% and 87.0% of the total nitrogen loss, respectively, and the runoff and nitrogen losses from the surface flow accounted for a high proportion. Compared to grassland, the Q. acutissima forest land showed significantly increased interflow and decreased surface flow and nitrogen loss. 参考文献 相似文献 引证文献

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To predict the occurrence of emergencies of man-made character in the state widely used methods of regression analysis. The regression model of such a process is usually non-linear. It is substantiated that the regression model of the occurrence of emergencies of man-made character should be presented in the form of a power polynomial. At the same time, the degree of polynomial should be about five times less than the number of statistical data.When estimating the parameters of a model using the least squares method, the dispersion of residuals for each observation or group of observations is not always ensured. This leads to the fact that the parameters of the regression model will not have a minimum dispersion, which degrades the forcast accuracy.The article improves the method of determining the predictive value of the number of man-made emergency situations taking into account the forecast of errors in the regression model and refining the estimates of its parameters on the basis of the weighted method of least squares, which allows to improve the accuracy of the forecast.The model of predicting of emergencies of man-made character on the basis of the weighted method of least squares is proposed, which differs in that it takes into account the error forecast of the sample regression model On the basis of the statistical data of the monitoring of emergencies of man-made character in Ukraine, experimental studies have been carried out on the effectiveness of applying the weighted method of least squares to improve the accuracy of the forecast using regression models. As a result of the research it has been established that the method allows increasing the accuracy of the forecast of emergencies of man-made character in the state due to the prediction of model errors and the refinement of its parameters by a weighted method of least squares by 4%As a benchmark for the comparative analysis, the average value of the forecast error module has been selected for the statistical data of the monitoring of emergencies of man-made character in Ukraine during the observation period.

Performance evaluation of base-isolated structures with sliding hydromagnetic bearings

Being an efficient technique for mitigating the seismic response of structures, base isolation is widely used in earthquake engineering practice. The sliding hydromagnetic bearing is viewed as a promising isolation system for seismic protection, owing to its adaptive damping energy dissipation, mild deformation constraint, and easy assembly and maintenance. To verify the applicability and efficiency of sliding hydromagnetic bearings, a performance evaluation of base-isolated structures with a sliding hydromagnetic base-isolation system is carried out in this paper. Numerical simulations are performed to explore the dynamic behaviors of sliding hydromagnetic bearings fabricated recently, for which two models, the power function and polynomial models, are proposed. Parameter identification and model validation are carried out using the data from numerical simulations and quasi-static tests. Backward differential formulas are employed to solve the stiff differential equation invoked by the Coulomb friction associated with the models, which bypasses the computational challenges inherent in conventional integral schemes. For a real-time definition of the instantaneous frequency in the models, the Hilbert–Huang transform is utilized. Comparative studies reveal that the sliding hydromagnetic bearing has an advantage over the lead rubber bearing and the curved surface slider in the control of structural displacement, structural velocity, and structural acceleration. Furthermore, the residual displacement yielded in the sliding hydromagnetic base-isolation system merely shifts the starting position of the bearing on the next movement, and the sliding surface and deformation constraints remain approximately as the initial condition.

Analytic study on optical solitons in parity-time-symmetric mixed linear and nonlinear modulation lattices with non-Kerr nonlinearities

This paper studies soliton solutions in parity-time-symmetric mixed linear and nonlinear optical lattices with Kerr and non-Kerr law nonlinearities. Four different kinds of rough mediums namely, parabolic law, power law, dual power law and polynomial law are considered in the context of non-Kerr media. With the help of the inverse engineering scheme, different types of soliton solutions are presented. The extracted outcomes show that exact bright and dark soliton solutions can exist for those different physical states.

Improving Landscape Spacious Development

The purpose of research resulted in recommendations development for landscapes spatial and territory organization improvement, in particular, on the basis of fields geometric parameters influence analysis. The conducted researches are focused on ordering of arable land territory, having spatial and territory unfavorable conditions for management. Analysis is carried out and estimation of fields geometrical parameters influence on mechanized cultivation is provided. The scale for assessing feasibility of crop rotation separating triangular form fields into trapezoidal form workspaces was formed. Different forms triangular plots (rectangular, equilateral, isosceles, scalene) and areas (from 6 to 72 ha) are considered during the study. For a comprehensive analysis of design decisions, economic indicators were used, namely: capital expenditures, annual expenses, additional products cost. Power polynomials were used to establish trends and describe the functional relationship between the different shapes of land plots area and the annual profit, resulted expenses and payback period. They were described by equations and graphs were constructed. Unprofitable, ineffective, expedient and optimal division of the triangular different types areas into trapezoidal form workspaces are presented in the table. The obtained results can be used in land management projects development for territories spatial development, territory organization, rational use organization and land protection.

Методика синтеза моделей зависимостей дисперсионных характеристик от частоты и состава оптического волокна

The article is devoted to the development of methods for the synthesis of models of the dependence of the refractive index on several parameters. The problem is solved with respect to the dependence of the refractive index on the frequency and concentration of alloying additives. As the initial dependence, the three-term Selmeyer formula is adopted. It is shown that the optimal model of the desired dependence is the representation in the form of a two-dimensional power polynomial. In this case, the dependence on the concentration of alloying additives is limited to the first degree. Frequency dependence is limited to the third degree. This view allows us to recommend the results obtained for engineering applications. Identification of models is carried out by the method of least squares with a balance of orders. Such a technique makes it possible to improve the conditionality of the corresponding information matrices. Also, a method for decomposing solutions to large-dimensional problems is proposed. This method allows us to reduce the solution of overdetermined systems of linear equations of order MxM to the solution of 2xM systems with M equations in each. The obtained numerical results have a high degree of interpolation accuracy and extrapolation stability. The offered methodology is approved for a next certain case. As alloying addition there is the chosen dioxide of germanium. As empiric data the values of the sought after parameters are got with the use of trinomial formula of Selmeyer. The values of coefficients of formula of Selmeyer are taken from well-known literary sources. Content of dioxide of germanium here changed from 0% to 13,5 %. As a trial selection the values of the interpolated and extrapolated parameters were used for maintenance of dioxide of germanium from 0% to 7,9%. Extrapolation was executed for the concentration of dioxide of germanium of 13,5%. The values of frequency for the construction of all models got out in a range from 175 ТГц to 375 ТГц. It approximately answers the working range of lengths of waves in the systems of transmission from 800 нм to 1700 нм. As dispersible descriptions considered: index of refraction, group index of refraction and group speed. The values of coefficients of two-dimensional models of dependences of these descriptions are got from frequency and concentration of alloying additions of dioxide of germanium.

CALCULATION OF POLYNOMIAL RATIO APPROXIMATED SURFACES OF BIFOCAL LENS

General imperfection of existent synthesis methods of bifocal lens surface is use complexity emerging over lack of analytical solution. Method of successive approximations is relatively simple, its main problem is determination of power polynomial coefficient approximating illuminated and shadow surface of being synthesized lens. To solve this problem it is suggest analytical determination method of polynomial coefficient approximating illuminated and shadow surface of bifocal lens. This method based on equality condition of electric path length of edge beam and beam passing through lens center. It is obtained analytical equation which permit to determine interdependence polynomials coefficients approximating illuminated and shadow surface of bifocal lens. Moreover, been finded equation allow to calculate bifocal lens thickness, that impossible using known methods of synthesis methods of bifocal lens surface. Cross-section of bifocal lens was be calculated with being suggested analytical method.

Modified response surface method basis harmony search to predict the burst pressure of corroded pipelines

Abstract The accurate burst pressure prediction of pipelines with corrosion defects is important to provide a suitable design of water, oil, and gas pipes networks. Generally, the empirical burst pressure models for corroded pipelines have the narrow limitation for large-verity of steel grades. In this paper, a modified response surface model is proposed based on the novel learning procedure using harmony search algorithm to predict the burst pressure of corroded pipelines with different steel grades named as HS-MRSM. The nonlinear relation as a power and high-order polynomial functions is calibrated using improved harmony search for large experimental corroded pipes >572 in HS-MRSM model. The performances for both accuracy and agreement predictions of the HS-MRSM are compared with modified response surface method (MRSM) and existing empirical models using comparative statistics as root mean square error (RMSE), mean absolute error (MAE), the Nash-Sutcliffe Efficiency (NSE), and the Willmott index of agreement (d). The results demonstrated that the proposed HS-MRSM is significantly improved The burst pressure predictions of corroded pipelines compared to best empirical model and MRSM. Generally, the empirical models – based PCORRC format are performed the best predictions among other empirical models.

Dynamic analysis of laminated doubly-curved shells with general boundary conditions by means of a domain decomposition method

The purpose of this paper is to study dynamic analysis of composite laminated doubly-curved shells with various boundary conditions by a domain decomposition method. Multi-segment partitioning technique is used to establish the formulation based on the first-order shear deformation theory. Meanwhile, the interfacial potential energy is introduced to maintain the continuous condition on the contact surface of the adjacent segments. The displacement admissible functions for each doubly-curved shell segment are uniformly expanded to the double mixed series which is with the Fourier series along the circumferential direction and the orthogonal polynomials (i.e. Chebyshev orthogonal polynomial, Legendre orthogonal polynomials and Ordinary power polynomials) along the meridional direction. A series of numerical examples are given for the free vibration, steady-state vibration and transient vibration of laminated doubly-curved shells subject to different geometric and material constants. By comparing with the literature results and the results conducted by the general finite element program ABAQUS, the numerical results show that the present formulation has good computational accuracy and efficiency. Based on the verification, the effect of external forces, geometric and material parameters on dynamic analysis (free, steady-state and transient vibration) of laminated doubly-curved shells are also studied.

Comparative Study on Water Permeability of Concrete Using Cylindrical Chamber Method and British Standard and Its Relation with Compressive Strength

Since the penetration of fluids (water, oil and chemicals) into concrete, plays a major role in the durability of concrete, this paper describes the effect of compressive strength of concrete on its permeability. Having revised the existing methods developed so far, the results of investigations into the permeability of different mixtures of concrete are presented. The results of the new method (cylindrical chamber method) used for the estimation of the permeability of 5 different strength grades concrete samples after different curing periods were compared with the comparative results obtained using British standard method (BS EN 12390-8:2009). These experiments tend to indicate a very good correlation between the two sets of results. Based on the test results, higher water/cement ratio and shorter curing period result in decreased compressive strength and increased permeability. The correlations between compressive strength and permeability parameters (penetration depth, average penetration flow velocity, permeability coefficient and penetration volume) are also investigated using a regression approach. It is concluded that power and second-order polynomial approximations can predict these correlations with a desirable accuracy.

Research in Area of Longevity of Sylphon Scraies

The proposed method of determining the sensitivity threshold for bellows expansion compensator by fitting a power polynomial of the empirical curves of distribution of durability for a large number of samples, followed by statistical analysis. For a reliable justification of resource products with regard to dispersion of their durability is of great importance the evaluation of the sensitivity threshold in cycles. Currently, the appointment of a guaranteed resource is made with high strength requirements. The proposed method allows to define sensitivity threshold value for the cycles between the curves of the distribution of longevity as having a distinct threshold, and not having it. Method is in good agreement with other known methods. Thus, by statistical processing of results of fatigue tests of joints obtained values of the sensitivity threshold in cycles and confidence interval for mathematical expectation of the magnitude of the threshold.

Robust dynamic optimization in heterogeneous multiscale catalytic flow reactors using polynomial chaos expansion

This paper explores the application of optimal design and operational strategies under uncertainty to a transient multiscale catalytic flow reactor system. The catalytic reactor is modeled using a spatially-dependent multiscale model that comprises lattice-based kinetic Monte Carlo (kMC) models coupled with continuum partial differential equations (PDEs) to account for the fine-scale and the macroscale reactor behaviour, respectively. This work compares two uncertainty propagation techniques, power series expansion (PSE) and polynomial chaos expansion (PCE), to assess their performance in multiscale process systems. The analysis reveals that PCE provides accurate results at minimal computational cost for the multiscale catalytic reactor model under the conditions considered in this work. PCE is subsequently used to perform robust dynamic optimization studies on the catalytic reactor system under uncertainty. The first study determines the optimal temperature trajectories that maximize the reactor’s performance under uncertainty. The second study aims to identify the optimal design and operating policies that allow the reactor, under uncertainty in the multiscale model parameters, to meet targeted performance specifications within a level of confidence. Both studies illustrate the benefits of performing dynamic optimization studies to improve performance for multiscale process systems under uncertainty.

Stochastic Fatigue Crack Growth Analysis for Space System Reliability

Abstract In this study, stochastic analysis is aimed for space structures (satellite in low earth orbit, made of aluminum 2024-T3), with the focus on fatigue failure. Primarily, the deterministic fatigue simulation is conducted using Walker and Forman models with constant amplitude loading. Deterministic crack growth was numerically simulated by the authors developed algorithm and is compared with commercial software for accuracy verification as well as validation with the experimental data. For the stochastic fatigue analysis of this study, uncertainty is estimated by using the Monte Carlo simulation. It is observed that by increasing the crack length, the standard deviation (the measure of uncertainty) increases. Also, it is noted that the reduction in stress ratio has the similar effect. Then, stochastic crack growth model, proposed by Yang and Manning, is employed for the reliability analysis. This model converts the existing deterministic fatigue models to stochastic one by adding a random coefficient. Applicability of this stochastic model completely depends on accuracy of base deterministic function. In this study, existing deterministic functions (power and second polynomial) are reviewed, and three new functions, (i) fractional, (ii) global, and (iii) exponential, are proposed. It is shown that the proposed functions are potentially used in the Yang and Manning model for better results.

Avaliação de curvas de crescimento em suínos

Objetivou-se simular pesos de suínos machos e fêmeas (de 1 a 157 dias de idade) através da distribuição de probabilidade uniforme num intervalo [a,b]. Foram ajustados os modelos de regressão (logístico, potência, tangente hiperbólica, gamma e polinomial cúbico) para explicar a possível relação do peso com o número de dias dos suínos. Verificou-se que os modelos logístico, gamma e polinomial cúbico apresentaram as melhores estimativas para explicar o comportamento do peso dos suínos machos e fêmeas. O modelo logístico apresentou R²= 0,975 e AIC=13,34 para os machos e R²= 0,9787 e AIC= 10,16 para as fêmeas. O modelo gamma apresentou grau de explicação de R²= 0,991 e AIC= 99,33 para os machos e R²= 0,9941 e AIC= 90,602 para as fêmeas, enquanto que o modelo polinomial cúbico apresentou R= 0,9995 e AIC=64,2 para os machos e R²= 0,9995 e AIC= 31,728 para as fêmeas. Optou-se pelo modelo polinomial cúbico para explicar o comportamento do peso simulado dos suínos, pois o mesmo apresentou R² alto e baixo AIC além de menos parâmetros que os outros modelos.

Derivative Kernels: Numerics and Applications.

A generalized framework for numerical differentiation (ND) is proposed for constructing a finite impulse response (FIR) filter in closed form. The framework regulates the frequency response of ND filters for arbitrary derivative-order and cutoff frequency selected parameters relying on interpolating power polynomials and maximally flat design techniques. Compared with the state-of-the-art solutions, such as Gaussian kernels, the proposed ND filter is sharply localized in the Fourier domain with ripple-free artifacts. Here, we construct 2D MaxFlat kernels for image directional differentiation to calculate image differentials for arbitrary derivative order, cutoff level and steering angle. The resulted kernel library renders a new solution capable of delivering discrete approximation of gradients, Hessian, and higher-order tensors in numerous applications. We tested the utility of this library on three different imaging applications with main focus on the unsharp masking. The reported results highlight the high efficiency of the 2D MaxFlat kernel and its versatility with respect to robustness and parameter control accuracy.