Search Results (30)

Strawberry (Fragaria × ananassa Duch.) production can be evaluated as repeated measurements, since the same plant is harvested multiple times during the production season. The objectives were to evaluate the production of fresh mass and fruit number in successive harvests and compare three strawberry clones in two cultivation conditions. Two experiments were carried out in two environmental cultivations: the rural property and the experimental area of the Plant Science Department, Federal University of Santa Maria, Brazil. The parameters of the nonlinear logistic model and their critical points were estimated via bootstrap for each condition and clone for fresh mass and fruit number with accumulated values, depending on the thermal sum accumulated during the production season. For nonlinear regression analysis, the ordinary least squares method was used with the Gauss–Newton algorithm. Confidence intervals were obtained for each parameter and estimated critical points, and they did not cross; the treatments were considered different. There were significant differences between clones and cultivation conditions for fruit mass and number. The nonlinear logistic models, adjusted for mass and number of strawberry fruits, detailed the production season, highlighting the main differences between cultivation conditions and clones. Full article

Fractional differential operators are inherently non-local, so global methods, such as spectral methods, are well suited for handling these non-local operators. Long-time integration of differential models such as chaotic dynamical systems poses specific challenges and considerations that make multi-domain numerical methods advantageous when dealing with such problems. This study proposes a novel multi-domain pseudospectral method based on the first kind of Chebyshev polynomials and the Gauss–Lobatto quadrature for fractional initial value problems.The proposed technique involves partitioning the problem’s domain into non-overlapping sub-domains, calculating the fractional differential operator in each sub-domain as the sum of the ‘local’ and ‘memory’ parts and deriving the corresponding differentiation matrices to develop the numerical schemes. The linear stability analysis indicates that the numerical scheme is absolutely stable for certain values of arbitrary non-integer order and conditionally stable for others. Numerical examples, ranging from single linear equations to systems of non-linear equations, demonstrate that the multi-domain approach is more appropriate, efficient and accurate than the single-domain scheme, particularly for problems with long-term dynamics. Full article

The Earth’s synthetic gravitational and density models can be used to validate numerical procedures applied for global (or large-scale regional) gravimetric forward and inverse modeling. Since the Earth’s lithospheric structure is better constrained by tomographic surveys than a deep mantle, most existing 3D density models describe only a lithospheric density structure, while 1D density models are typically used to describe a deep mantle density structure below the lithosphere-asthenosphere boundary. The accuracy of currently available lithospheric density models is examined in this study. The error analysis is established to assess the accuracy of modeling the sub-lithospheric mantle geoid while focusing on the largest errors (according to our estimates) that are attributed to lithospheric thickness and lithospheric mantle density uncertainties. Since a forward modeling of the sub-lithospheric mantle geoid also comprises numerical procedures of adding and subtracting gravitational contributions of similar density structures, the error propagation is derived for actual rather than random errors (that are described by the Gauss’ error propagation law). Possible systematic errors then either lessen or sum up after applying particular corrections to a geoidal geometry that are attributed to individual lithospheric density structures (such as sediments) or density interfaces (such as a Moho density contrast). The analysis indicates that errors in modeling of the sub-lithospheric mantle geoid attributed to lithospheric thickness and lithospheric mantle density uncertainties could reach several hundreds of meters, particularly at locations with the largest lithospheric thickness under cratonic formations. This numerical finding is important for the calibration and further development of synthetic density models of which mass equals the Earth’s total mass (excluding the atmosphere). Consequently, the (long-to-medium wavelength) gravitational field generated by a synthetic density model should closely agree with the Earth’s gravitational field. Full article

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on the accurate estimation and parameter calibration of DER_A, a recently proposed aggregated IBDER model. In particular, we focus on the parameters of the reactive power–voltage regulation module. We formulate the problem of parameter tuning as a non-linear least square minimization problem and solve it using the Levenberg–Marquardt (LM) method. The LM method is primarily chosen due to its flexibility in adaptively selecting between the steepest descent and Gauss–Newton methods through a damping parameter. The LM approach is used to minimize the error between the actual measurements and the estimated response of the model. Further, the computational challenges posed by the numerical calculation of the Jacobian are tackled using a quasi-Newton root-finding approach. The proposed method is validated on a real feeder model in the northeastern part of the United States. The feeder is modeled in OpenDSS and the measurements thus obtained are fed to the DER_A model for calibration. The simulation results indicate that our approach is able to successfully calibrate the relevant model parameters quickly and with high accuracy, with a total sum of square error of $3.57\times {10}^{-7}$. Full article

The Hermean average perihelion rate ${\dot{\omega }}^2\mathrm{PN}$, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from $-18$ to $-4$ microarcseconds per century $\left(\mu \mathrm{as}{\mathrm{cty}}^{-1}\right)$, depending on the true anomaly at epoch $f_0$. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun’s gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury’s perihelion rate ${\dot{\omega }}_{\exp }$ recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is ${\sigma }_{{\dot{\omega }}_{\exp }}\simeq 8\mu \mathrm{as}{\mathrm{cty}}^{-1}$, corresponding to a relative accuracy of $2\times {10}^{-7}$ for the combination $\left(2+2\gamma -\beta \right)/3$ of the PPN parameters $\beta$ and $\gamma$ scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to ≃10–50 times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recently improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a $\simeq {10}^{-7}$ accuracy level in constraining $\beta$ and $\gamma$ in an extended mission, despite $\simeq {10}^{-6}$ seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not-too-distant future, it will be necessary to include the 2PN acceleration in the Solar System’s dynamics as well. Full article

Numerical simulation and inversion imaging are essential in geophysics exploration. Fourier transform plays a vital role in geophysical numerical simulation and inversion imaging, especially in solving partial differential equations. This paper proposes an arbitrary sampling Fourier transform algorithm (AS-FT) based on quadratic interpolation of shape function. Its core idea is to discretize the Fourier transform integral into the sum of finite element integrals. The quadratic shape function represents the function change in each element, and then all element integrals are calculated and accumulated. In this way, the semi-analytical solution of the Fourier oscillation operator in each integral interval can be obtained, and the Fourier transform coefficient can be calculated in advance, so the algorithm has high calculation accuracy and efficiency. Based on the one-dimensional (1D) transform, the two-dimensional (2D) transform is realized by integrating the 1D Fourier transform twice, and the three-dimensional (3D) transform is realized by integrating the 1D Fourier transform three times. The algorithm can sample flexibly according to the distribution of integrated values. The correctness and efficiency of the algorithm are verified by Fourier transform pairs. The AS-FT algorithm is applied to the numerical simulation of magnetic anomalies. The accuracy and efficiency are compared with the standard Fast Fourier transform (standard-FFT) and Gauss Fast Fourier transform (Gauss-FFT). It shows that the AS-FT algorithm has no edge effects and has a higher computational speed. The AS-FT algorithm has good adaptability to continuous medium, weak magnetic catastrophe medium, and strong magnetic catastrophe medium. It can achieve the same as or even higher accuracy than Gauss-FFT through fewer sampling points. The AS-FT algorithm provides a new means for partial differential equation solution in geophysics. It successfully solves the boundary problems, which makes it an efficient and high-precision Fourier transform approach with promising applications. Therefore, the AS-FT algorithm has excellent advantages in solving partial differential equations, providing a new means for solving geophysical forward and inverse problems. Full article

The evaluation of baroreflex sensitivity (BRS) has proven to be critical for medical applications. The use of α indices by spectral methods has been the most popular approach to BRS estimation. Recently, an algorithm termed Gaussian average filtering decomposition (GAFD) has been proposed to serve the same purpose. GAFD adopts a three-layer tree structure similar to wavelet decomposition but is only constructed by Gaussian windows in different cutoff frequency. Its computation is more efficient than that of conventional spectral methods, and there is no need to specify any parameter. This research presents a novel approach, referred to as modulated Gaussian filter (modGauss) for BRS estimation. It has a more simplified structure than GAFD using only two bandpass filters of dedicated passbands, so that the three-level structure in GAFD is avoided. This strategy makes modGauss more efficient than GAFD in computation, while the advantages of GAFD are preserved. Both GAFD and modGauss are conducted extensively in the time domain, yet can achieve similar results to conventional spectral methods. In computational simulations, the EuroBavar dataset was used to assess the performance of the novel algorithm. The BRS values were calculated by four other methods (three spectral approaches and GAFD) for performance comparison. From a comparison using the Wilcoxon rank sum test, it was found that there was no statistically significant dissimilarity; instead, very good agreement using the intraclass correlation coefficient (ICC) was observed. The modGauss algorithm was also found to be the fastest in computation time and suitable for the long-term estimation of BRS. The novel algorithm, as described in this report, can be applied in medical equipment for real-time estimation of BRS in clinical settings. Full article

This paper designs a new finite difference compact reconstruction unequal-sized weighted essentially nonoscillatory scheme (CRUS-WENO) for solving fractional differential equations containing the fractional Laplacian operator. This new CRUS-WENO scheme uses stencils of different sizes to achieve fifth-order accuracy in smooth regions and maintain nonoscillatory properties near discontinuities. The fractional Laplacian operator of order $\beta$$(0<\beta <1)$ is split into the integral part and the first derivative term. Using the Gauss–Jacobi quadrature method to solve the integral part of the fractional Laplacian operators, a new finite difference CRUS-WENO scheme is presented to discretize the first derivative term of the fractional equation. This new CRUS-WENO scheme has the advantages of a narrower large stencil and high spectral resolution. In addition, the linear weights of the new CRUS-WENO scheme can be any positive numbers whose sum is one, which greatly reduces the calculation cost. Some numerical examples are given to show the effectiveness and feasibility of this new CRUS-WENO scheme in solving fractional equations containing the fractional Laplacian operator. Full article

This work proposes a unifying framework for extending PDE-constrained Large Deformation Diffeomorphic Metric Mapping (PDE-LDDMM) with the sum of squared differences (SSD) to PDE-LDDMM with different image similarity metrics. We focused on the two best-performing variants of PDE-LDDMM with the spatial and band-limited parameterizations of diffeomorphisms. We derived the equations for gradient-descent and Gauss–Newton–Krylov (GNK) optimization with Normalized Cross-Correlation (NCC), its local version (lNCC), Normalized Gradient Fields (NGFs), and Mutual Information (MI). PDE-LDDMM with GNK was successfully implemented for NCC and lNCC, substantially improving the registration results of SSD. For these metrics, GNK optimization outperformed gradient-descent. However, for NGFs, GNK optimization was not able to overpass the performance of gradient-descent. For MI, GNK optimization involved the product of huge dense matrices, requesting an unaffordable memory load. The extensive evaluation reported the band-limited version of PDE-LDDMM based on the deformation state equation with NCC and lNCC image similarities among the best performing PDE-LDDMM methods. In comparison with benchmark deep learning-based methods, our proposal reached or surpassed the accuracy of the best-performing models. In NIREP16, several configurations of PDE-LDDMM outperformed ANTS-lNCC, the best benchmark method. Although NGFs and MI usually underperformed the other metrics in our evaluation, these metrics showed potentially competitive results in a multimodal deformable experiment. We believe that our proposed image similarity extension over PDE-LDDMM will promote the use of physically meaningful diffeomorphisms in a wide variety of clinical applications depending on deformable image registration. Full article

Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss–Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations. Full article

The impulse response of the fractional oscillation equation was investigated, where the damping term was characterized by means of the Riemann–Liouville fractional derivative with the order $\alpha$ satisfying $0\le \alpha \le 2$. Two different analytical forms of the response were obtained by using the two different methods of inverse Laplace transform. The first analytical form is a series composed of positive powers of t, which converges rapidly for a small t. The second form is a sum of a damped harmonic oscillation with negative exponential amplitude and a decayed function in the form of an infinite integral, where the infinite integral converges rapidly for a large t. Furthermore, the Gauss–Laguerre quadrature formula was used for numerical calculation of the infinite integral to generate an analytical approximation to the response. The asymptotic behaviours for a small t and large t were obtained from the two forms of response. The second form provides more details for the response and is applicable for a larger range of t. The results include that of the integer-order cases, $\alpha =$ 0, 1 and 2. Full article

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p. Full article

The aim of the present paper is to analyze the viability of using Lorentz Force (LF) acting on a charged spacecraft to neutralize the effects of Solar Radiation Pressure (SRP) on the longitude of the ascending node and the argument of perigee of the spacecraft’s orbit. In this setting, the Gauss planetary equations for LF and SRP are presented and averaged over the true anomaly. The averaged variations for the longitude of the ascending node (h) and the argument of perigee (g) are invariant under the symmetry $(i,g)⟶(-i,-g)$ due to Lorentz Force. The sum of change rates due to both perturbing forces of LF and SRP is assigned by zero to estimate the charge amount to balance the variation for the argument of perigee and longitude of ascending. Numerical investigations have been developed to show the evolution of the charge quantity for different orbital parameters at both Low Earth and Geosynchronous Orbits. Full article

When a straight cylindrical conductor of finite length is electrostatically charged, its electrostatic potential $\varphi$ depends on the electrostatic charge $q_e$, as expressed by the equation $\mathcal{L}\left(q_e\right)=\varphi$, where $\mathcal{L}$ is an integral operator. Method of moments (MoM) is an excellent candidate for solving $\mathcal{L}\left(q_e\right)=\varphi$ numerically. In fact, considering $q_e$ as a piece-wise constant over the length of the conductor, it can be expressed as a finite series of weighted basis functions, $q_e={\sum }_{n=1}^N{\alpha }_n{f}_n$ (with weights ${\alpha }_n$ and N, number of the subsections of the conductor) defined in the $\mathcal{L}$ domain so that $\varphi$ becomes a finite sum of integrals from which, considering testing functions suitably combined with the basis functions, one obtains an algebraic system $L_{mn}{\alpha }_n=g_m$ with dense matrix, equivalent to $\mathcal{L}\left(q_e\right)=\varphi$. Once solved, the linear algebraic system gets ${\alpha }_n$ and therefore $q_e$ is obtainable so that the electrostatic capacitance $C=q_e/V$, where V is the external electrical tension applied, can give the corresponding electrostatic capacitance. In this paper, a comparison was made among some Krylov subspace method-based procedures to solve $L_{mn}{\alpha }_n=g_m$. These methods have, as a basic idea, the projection of a problem related to a matrix $A\in {\mathbb{R}}^{n\times n}$, having a number of non-null elements of the order of n, in a subspace of lower order. This reduces the computational complexity of the algorithms for solving linear algebraic systems in which the matrix is dense. Five cases were identified to determine $L_{mn}$ according to the type of basis-testing functions pair used. In particular: (1) pulse function as the basis function and delta function as the testing function; (2) pulse function as the basis function as well as testing function; (3) triangular function as the basis function and delta function as the testing function; (4) triangular function as the basis function and pulse function as the testing function; (5) triangular function as the basis function with the Galerkin Procedure. Therefore, five $L_{mn}$ and five pair $q_e$ and C were computed. For each case, for the resolution of $L_{mn}{\alpha }_n=g_m$ obtained, GMRES, CGS, and BicGStab algorithms (based on Krylov subspaces approach) were implemented in the MatLab® Toolbox to evaluate $q_e$ and C as N increases, highlighting asymptotical behaviors of the procedures. Then, a particular value for N is obtained, exploiting both the conditioning number of $L_{mn}$ and considerations on C, to avoid instability phenomena. The performances of the exploited procedures have been evaluated in terms of convergence speed and CPU-times as the length/diameter and N increase. The results show the superiority of BcGStab, compared to the other procedures used, since even if the number of iterations increases significantly, the CPU-time decreases (more than 50%) when the asymptotic behavior of all the procedures is in place. This superiority is much more evident when the CPU-time of BicGStab is compared with that achieved by exploiting Gauss elimination and Gauss–Seidel approaches. Full article

In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo p, where p be an odd prime with $p=8k+1$ or $p=12k+1$. Full article