Journal articles: 'Sinc points'

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Youssef, Maha, Hany A. El-Sharkawy, and Gerd Baumann. "Lebesgue Constant Using Sinc Points." Advances in Numerical Analysis 2016 (September 19, 2016): 1–10. http://dx.doi.org/10.1155/2016/6758283.

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Lebesgue constant for Lagrange approximation at Sinc points will be examined. We introduce a new barycentric form for Lagrange approximation at Sinc points. Using Thiele’s algorithm we show that the Lebesgue constant grows logarithmically as the number of interpolation Sinc points increases. A comparison between the obtained upper bound of Lebesgue constant using Sinc points and other upper bounds for different set of points, like equidistant and Chebyshev points, is introduced.

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M., Youssef, and Baumann G. "Collocation Method to Solve Elliptic Equations Bivariate Poly-Sinc Approximation." Journal of Progressive Research in Mathematics 7, no. 3 (2016): 1079–91. https://doi.org/10.5281/zenodo.3977340.

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The paper proposes a collocation method to solve bivariate elliptic partial differential equations. The method uses Lagrange approximation based on Sinc point collocations. The proposed approximation is collocating on non-equidistant interpolation points generated by conformal maps, called Sinc points. We prove the upper bound of the error for the bivariate Lagrange approximation at these Sinc points. Then we define a collocation algorithm using this approximation to solve elliptic PDEs. We verify the Poly-Sinc technique for different elliptic equations and compare the approximate solutions with exact solutions.

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Khalil, Omar, Hany El-Sharkawy, Maha Youssef, and Gerd Baumann. "Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations." Algorithms 15, no. 9 (2022): 320. http://dx.doi.org/10.3390/a15090320.

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We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations.

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Khalil, Omar A., and Gerd Baumann. "An h-Adaptive Poly-Sinc-Based Local Discontinuous Galerkin Method for Elliptic Partial Differential Equations." Axioms 12, no. 3 (2023): 227. http://dx.doi.org/10.3390/axioms12030227.

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For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points. The adaptive approach, which uses Poly-Sinc interpolation to achieve a predetermined level of approximation accuracy, is a local discontinuous Galerkin method. We developed an a priori error estimate and demonstrated the exponential convergence of the Poly-Sinc-based discontinuous Galerkin technique, as well as the adaptive piecewise Poly-Sinc method, for function approximation and ordinary differential equations. In this paper, we demonstrate the exponential convergence in the number of iterations of the a priori error estimate derived for the local discontinuous Galerkin technique under the condition that a reliable estimate of the precise solution of the partial differential equation at the Sinc points exists. For the purpose of refining the computational domain, we employ a statistical strategy. The numerical results for elliptic PDEs with Dirichlet and mixed Neumann-Dirichlet boundary conditions are demonstrated to validate the adaptive greedy Poly-Sinc approach.

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Youssef, Maha, Hany A. El-Sharkawy, and Gerd Baumann. "Multivariate Lagrange Interpolation at Sinc Points Error Estimation and Lebesgue Constant." Journal of Mathematics Research 8, no. 4 (2016): 118. http://dx.doi.org/10.5539/jmr.v8n4p118.

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This paper gives an explicit construction of multivariate Lagrange interpolation at Sinc points. A nested operator formula for Lagrange interpolation over an $m$-dimensional region is introduced. For the nested Lagrange interpolation, a proof of the upper bound of the error is given showing that the error has an exponentially decaying behavior. For the uniform convergence the growth of the associated norms of the interpolation operator, i.e., the Lebesgue constant has to be taken into consideration. It turns out that this growth is of logarithmic nature $O((log n)^m)$. We compare the obtained Lebesgue constant bound with other well known bounds for Lebesgue constants using different set of points.

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Al sagheer, Aya Nadhim Abdul Hasan. "Numerical solution of singular Poisson equations using sinc approximation." Mustansiriyah Journal of Pure and Applied Sciences 2, no. 4 (2024): 41–48. http://dx.doi.org/10.47831/mjpas.2024.2.4.41-48.

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Abstract In this article, we use the Sinc approximation to solve the single Poisson problem (where the first derivative or higher order does not have an exact answer on the border of the boundary). We have examined the Sinc Galerkin approximation to solve the single Poisson problem, and finally, to solve the Poisson problem, we will use the sinc collocation method and in this method, we will reach a linear system. By carefully choosing the length of the steps and the number of nodal points, we will solve this system with two methods, with the orthogonalization technique, a numerical approximation will be obtained. Its accuracy can be exponential and of order where is a transaction parameter and c are a constant independent of N. In the final part, we will give some numerical examples of single Poisson problems.

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Al sagheer, Aya Nadhim Abdul Hasan. "Numerical solution of singular Poisson equations using sinc approximation." Mustansiriyah Journal of Pure and Applied Sciences 2, no. 4 (2024): 41–48. http://dx.doi.org/10.47831/mjpas.v2i4.136.

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Abstract In this article, we use the Sinc approximation to solve the single Poisson problem (where the first derivative or higher order does not have an exact answer on the border of the boundary). We have examined the Sinc Galerkin approximation to solve the single Poisson problem, and finally, to solve the Poisson problem, we will use the sinc collocation method and in this method, we will reach a linear system. By carefully choosing the length of the steps and the number of nodal points, we will solve this system with two methods, with the orthogonalization technique, a numerical approximation will be obtained. Its accuracy can be exponential and of order where is a transaction parameter and c are a constant independent of N. In the final part, we will give some numerical examples of single Poisson problems.

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Wang, Jixian, Zhangrong Mei, Yonghua Mao, Xiaohui Shi, and Guoquan Zhou. "High-Order Sinc-Correlated Model Vortex Beams." Photonics 10, no. 5 (2023): 550. http://dx.doi.org/10.3390/photonics10050550.

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We propose a new partially coherent vortex source model in which the spatial correlation function is a sinc function on the difference from the q-th power of the coordinates of two points of the source field. The beam radiated by such source is termed the high-order sinc-correlated model vortex (SCMV) beam. We derived the propagating formula of the cross-spectral density (CSD) function for SCMV beams in atmospheric disturbances. On the basis of the derived analytical expression, the behavior of the spectral density of the SCMV beams propagating in free space and atmosphere turbulence was investigated under comparative analysis. The results show that the spectral densities of such beams exhibited interesting novel features, which were significantly different from those of the trivial vortex beams.

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Ramos, Pedro, Fernando Janeiro, and Tomáš Radil. "Comparative Analysis of Three Algorithms for Two-Channel Common Frequency Sinewave Parameter Estimation: Ellipse Fit, Seven Parameter Sine Fit and Spectral Sinc Fit." Metrology and Measurement Systems 17, no. 2 (2010): 255–70. http://dx.doi.org/10.2478/v10178-010-0022-8.

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Comparative Analysis of Three Algorithms for Two-Channel Common Frequency Sinewave Parameter Estimation: Ellipse Fit, Seven Parameter Sine Fit and Spectral Sinc FitIn this paper, a comparison analysis of three different algorithms for the estimation of sine signal parameters in two-channel common frequency situations is presented. The relevance of this situation is clearly understood in multiple applications where the algorithms have been applied. They include impedance measurements, eddy currents testing, laser anemometry and radio receiver testing for example. The three algorithms belong to different categories because they are based on different approaches. The ellipse fit algorithm is a parametric fit based on the XY plot of the samples of both signals. The seven parameter sine fit algorithm is a least-squares algorithm based on the time domain fitting of a single tone sinewave model to the acquired samples. The spectral sinc fit performs a fitting in the frequency domain of the exact model of an acquired sinewave on the acquired spectrum. Multiple simulation situations and real measurements are included in the comparison to demonstrate the weaknesses and strong points of each algorithm.

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Barati, Ali, and Mohammad Nabati. "A numerical technique for solving a class of nonlinear singularly perturbed boundary value problems." Filomat 35, no. 10 (2021): 3353–64. http://dx.doi.org/10.2298/fil2110353b.

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In this work, we have studied a numerical scheme based on Sinc collocation method to solve a class of nonlinear singularly perturbed boundary value problems. The solution of the problems exhibit a boundary layer on the both sides or one side of the domain due to the presence of perturbation parameter ?. The Sinc method can control the oscillations in computed solutions at boundary layer regions naturally because the distribution of Sinc points is denser at near the boundaries. The convergence analysis is discussed and the method is shown to be an exponential convergent. The numerical results support the theoretical results and illustrate the efficiency and accuracy of the method compared with the results in the existing methods.

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Alkan, Sertan. "Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative." Thermal Science 25, Spec. issue 1 (2021): 121–30. http://dx.doi.org/10.2298/tsci200504013a.

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In this paper, it is presented that an approximate solution of a class of non-linear differential equations with conformable derivative under boundary conditions by using sinc-Galerkin method that is not used to approximately solve the class of the considered equation in the literature. In the method, the solution function is expressed as a finite series in terms of composite translated sinc functions and the unknown coefficients. The problem is reduced into a non-linear matrix-vector system via sinc grid points, and when this system is solved by using Newton?s method, the unknown coefficients of the solution function are easily obtained. Also, error analysis and some test problems are presented to illustrate the applicability and accuracy of the proposed method.

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Barati, Ali, and Ali Atabaigi. "Numerical solutions of a system of singularly perturbed reaction-diffusion problems." Filomat 33, no. 15 (2019): 4889–905. http://dx.doi.org/10.2298/fil1915889b.

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This paper addresses the numerical approximation of solutions to a coupled system of singularly perturbed reaction-diffusion equations. The components of the solution exhibit overlapping boundary and interior layers. Sinc procedure can control the oscillations in computed solutions at boundary layer regions naturally because the distribution of Sinc points is denser at near the boundaries. Also the obtained results show that the proposed method is applicable even for small perturbation parameter as ? = 2-30. The convergence analysis of proposed technique is discussed, it is shown that the approximate solutions converge to the exact solutions at an exponential rate. Numerical experiments are carried out to demonstrate the accuracy and efficiency of the method.

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Li, Zhengping, Chaoliang Qin, and Hao Shi. "Small-Range High-Precision Positioning Based on Two-Point Coordination for Robot." Mobile Information Systems 2021 (June 15, 2021): 1–6. http://dx.doi.org/10.1155/2021/8732006.

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This paper proposed a two-point coordinated positioning algorithm. Based on the assumption that the distance between two points was constant, a fusion algorithm was introduced into the positioning process to enhance the positioning accuracy. The simulation results showed that the proposed algorithm could reduce the RMS error to about 50% of the improved sinc interpolation-based positioning algorithm when the sampling frequency was 500 MHz and the interpolation number was 19.

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Al-Khaled, Kamel, and Nid’a M. Rababah. "Fast Convergence Methods for Hyperbolic Systems of Balance Laws with Riemann Conditions." Symmetry 12, no. 5 (2020): 757. http://dx.doi.org/10.3390/sym12050757.

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In this paper, we develop an accurate technique via the use of the Adomian decomposition method (ADM) to solve analytically a 2 × 2 systems of partial differential equation that represent balance laws of hyperbolic-elliptic type. We prove that the sequence of iteration obtained by ADM converges strongly to the exact solution by establishing a construction of fixed points. For comparison purposes, we also use the Sinc function methodology to establish a new procedure to solve numerically the same system. It is shown that approximation by Sinc function converges to the exact solution exponentially, also handles changes in type. A numerical example is presented to demonstrate the theoretical results. It is noted that the two methods show the symmetry in the approximate solution. The results obtained by both methods reveal that they are reliable and convenient for solving balance laws where the initial conditions are of the Riemann type.

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Kotera, Hiroaki. "Inverse-Scaled Lanczos Filtering for Image Sharpening." Color and Imaging Conference 2020, no. 28 (2020): 215–20. http://dx.doi.org/10.2352/issn.2169-2629.2020.28.34.

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The edge response in retinal image is the first step for human vision recognizing the outside world. A variety of receptive field models for describing the impulse response have been proposed. Which satisfies the uncertain principle? occupied the interest from a point of minimizing the product (Δx)(Δ w) both in spatial and spectral. Among the typical edge response models, finally Gabor function and 2nd. Gaussian Derivative GD2 remained as strong candidates. While famous D. Marr and R. Young support GD2, many vision researchers prefer Gabor. The retinal edge response model is used for image sharpening.<br/> Different from the conventional image sharpening filters, this paper proposes a novel image sharpening filter by modifying the Lanczos resampling filter. The Lanczos filter is used for image scaling to resize digital images. Usually it works to interpolate the discrete sampled points like as a kind of smoothing filter not as sharpening. The Lanczos kernel is given by the product of sampling Sinc function and the scaled Sinc function. The scaled Sinc function expanded by the scale "s" plays a role of window function. The author noticed that the inverse scaling of Lanczos window can be used not for smoothing but for sharpening filter.<br/> This paper demonstrates how the proposed model works effectively in comparison with Gabor and GD2.

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Tanaka, Ken’ichiro, and Masaaki Sugihara. "Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization." IMA Journal of Numerical Analysis 39, no. 4 (2018): 1957–84. http://dx.doi.org/10.1093/imanum/dry056.

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Abstract We propose a simple and effective method for designing approximation formulas for weighted analytic functions. We consider spaces of such functions according to weight functions expressing the decay properties of the functions. Then we adopt the minimum worst error of the $n$-point approximation formulas in each space for characterizing the optimal sampling points for the approximation. In order to obtain approximately optimal sampling points we consider minimization of a discrete energy related to the minimum worst error. Consequently, we obtain an approximation formula and its theoretical error estimate in each space. In addition, from some numerical experiments, we observe that the formula generated by the proposed method outperforms the corresponding formula derived with sinc approximation, which is near optimal in each space.

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Haavik, Kjetil E. "Extended use of receiver groups: Theory, synthetic example, and noise considerations." GEOPHYSICS 85, no. 6 (2020): P53—P66. http://dx.doi.org/10.1190/geo2019-0624.1.

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Receiver grouping is commonly used in marine towed-streamer seismic acquisition. Measurements from several receivers in a group are stacked to increase the signal-to-noise ratio of the resulting data and form an analog spatial antialiasing filter. I propose a method for extracting inline derivatives of the wavefield as additional measurements from the groups. This is achieved by multiplying the signal from the individual receivers in a group with predefined weights that corresponds to a finite-difference (FD) operator. The inline derivative(s) makes it possible to use multichannel sampling theorems to reconstruct the signal on a denser grid. Extraction of FD data from clusters of receivers is not a new concept, but I find that, by using the geometry of conventional streamer groups, it is possible to obtain FD data which are well suited for multichannel interpolation. The key to finding suitable FD operators is to recognize that it is not the ideal differentiation response we seek, but the impulse response of the group multiplied with the ideal differentiation response. Furthermore, under a Gaussian noise assumption, I derive formulas for the resulting noise level from sinc and higher order sinc interpolations. I find that the random noise level in the reconstructed data, when using higher order sinc interpolation, is expected to be higher than when using conventional sinc interpolation and will vary with respect to the distance from the original sampling points. The statistical analysis shows that it is beneficial to find FD operators with as small an [Formula: see text] norm as possible. A synthetic example shows that the proposed method of extracting FD operators and subsequent interpolation works very well. I foresee that the proposed method can be used to reduce the density of receivers (hydrophones or geophones) when designing new streamers or with existing equipment to improve the inline sampling.

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Exl, Lukas, Claas Abert, Norbert J. Mauser, Thomas Schrefl, Hans Peter Stimming, and Dieter Suess. "FFT-based Kronecker product approximation to micromagnetic long-range interactions." Mathematical Models and Methods in Applied Sciences 24, no. 09 (2014): 1877–901. http://dx.doi.org/10.1142/s0218202514500109.

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We derive a Kronecker product approximation for the micromagnetic long-range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format, Tensor Trains) scales below linear in the volume size. Based on efficient usage of FFT for structured tensors, we are able to accelerate computations to quasi-linear complexity in the number of collocation points used in one dimension. Quadratic convergence of the underlying collocation scheme as well as exponential convergence in the separation rank of the approximations is proved. Numerical experiments on accuracy and complexity confirm the theoretical results.

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Zheng, Shuhui, Hang Zhou, Zhuohui Chen та ін. "Type III Transforming Growth Factor-β Receptor RNA Interference Enhances Transforming Growth Factor β3-Induced Chondrogenesis Signaling in Human Mesenchymal Stem Cells". Stem Cells International 2018 (8 серпня 2018): 1–11. http://dx.doi.org/10.1155/2018/4180857.

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The type III transforming growth factor-β (TGF-β) receptor (TβRIII), a coreceptor of the TGF-β superfamily, is known to bind TGF-βs and regulate TGF-β signaling. However, the regulatory roles of TβRIII in TGF-β-induced mesenchymal stem cell (MSC) chondrogenesis have not been explored. The present study examined the effect of TβRIII RNA interference (RNAi) on TGF-β3-induced human MSC (hMSC) chondrogenesis and possible signal mechanisms. A lentiviral expression vector containing TβRIII small interfering RNA (siRNA) (SiTβRIII) or a control siRNA (SiNC) gene was constructed and infected into hMSCs. The cells were cultured in chondrogenic medium containing TGF-β3 or control medium. TβRIII RNAi significantly enhanced TGF-β3-induced chondrogenic differentiation of hMSCs, the ratio of type II (TβRII) to type I (TβRI) TGF-β receptors, and phosphorylation levels of Smad2/3 as compared with cells infected with SiNC. An inhibitor of the TGF-β signal, SB431542, not only inhibited TβRIII RNAi-stimulated TGF-β3-mediated Smad2/3 phosphorylation but also inhibited the effects of TβRIII RNAi on TGF-β3-induced chondrogenic differentiation. These results demonstrate that TβRIII RNAi enhances TGF-β3-induced chondrogenic differentiation in hMSCs by activating TGF-β/Smad2/3 signaling. The finding points to the possibility of modifying MSCs by TβRIII knockdown as a potent future strategy for cell-based cartilage tissue engineering.

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Jia, Wei, Yuan Feng, Xingshuai Qiao, Tianrun Wang, and Tao Shan. "Variable Doppler Starting Point Keystone Transform for Radar Maneuvering Target Detection." Remote Sensing 16, no. 12 (2024): 2129. http://dx.doi.org/10.3390/rs16122129.

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The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address the aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving computational efficiency. Finally, the simulation and real data experiments demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

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Pollock, D. Stephen G. "Linear Stochastic Models in Discrete and Continuous Time." Econometrics 8, no. 3 (2020): 35. http://dx.doi.org/10.3390/econometrics8030035.

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The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of [0,π] radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described.

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Billings, Stephen D., Garry N. Newsam, and Rick K. Beatson. "Smooth fitting of geophysical data using continuous global surfaces." GEOPHYSICS 67, no. 6 (2002): 1823–34. http://dx.doi.org/10.1190/1.1527082.

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Continuous global surfaces (CGS) are a general framework for interpolation and smoothing of geophysical data. The first of two smoothing techniques we consider in this paper is generalized cross validation (GCV), which is a bootstrap measure of the predictive error of a surface that requires no prior knowledge of noise levels. The second smoothing technique is to define the CGS surface with fewer centers than data points, and compute the fit by least squares (LSQR); the noise levels are implicitly estimated by the number and placement of the centers relative to the data points. We show that both smoothing methods can be implemented using extensions to the existing fast framework for interpolation, so that it is now possible to construct realistic smooth fits to the very large data sets typically collected in geophysics. Thin‐plate spline and kriging surfaces with GCV smoothing appear to produce realistic fits to noisy radiometric data. The resulting surfaces are similar, yet the thin‐plate spline required less parameterization. Given the simplicity and parsimony of GCV, this makes a combination of the two methods a reasonable default choice for the smoothing problem. LSQR smooth fitting with sinc functions defined on a regular grid of centers, effectively low‐pass filters the data and produces a reasonable surface, although one not as visually appealing as for splines and kriging.

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Figueroa-Duran, Antonio, and Efren Fernandez-Grande. "Reconstruction of reverberant sound fields over large spatial domains." Journal of the Acoustical Society of America 157, no. 1 (2025): 180–90. https://doi.org/10.1121/10.0034833.

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Characterising acoustic fields in rooms is challenging due to the complexity of data acquisition. Sound field reconstruction methods aim at predicting the acoustic quantities at positions where no data are available, incorporating generalisable physical priors of the sound in a room. This study introduces a model that exploits the general time structure of the room impulse response, where a wave-based expansion addresses the direct sound and early reflections, localising their apparent origin, and kernel methods are applied to the late part. This late energy is considered to follow a sinc-like spatial correlation, in accordance with the random wave field theory. Synthesised pressure points, which follow the observed statistics of the sound field, are introduced to enable extrapolation over large distances. The model is evaluated experimentally in a lecture room and an auditorium, demonstrating a successful reconstruction of the sound field across a 5 m aperture using three microphone arrays of only 4.2 cm radius each. These results indicate that the proposed methodology enables volumetric extrapolation over several orders of magnitude, which is significant in the context of navigable sound field reproduction, “6-degrees of freedom” spatial audio and sound field analysis in rooms.

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Mei, Shuli, and Wanlin Gao. "Shannon–Cosine wavelet spectral method for solving fractional Fokker–Planck equations." International Journal of Wavelets, Multiresolution and Information Processing 16, no. 03 (2018): 1850021. http://dx.doi.org/10.1142/s0219691318500212.

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The windowed-Shannon wavelet is not recommended generally as the window function will destroy the partition of unity of Shannon mother wavelet. A novel windowing scheme is proposed to overcome the shortcoming of the general windowed-Shannon function, and then, a novel and efficient Shannon–Cosine wavelet spectral method is provided for solving the fractional PDEs. Taking full advantage of the waveform of sinc function to hold the partition of unity, Shannon–Cosine wavelet is constructed, which is composed of Shannon wavelet and the trigonometric polynomials. It was proved that the proposed wavelet function meets the requirements of being a trial function and possesses many other excellent properties such as normalization, interpolation, two-scale relations, compact support domain, and so on. Therefore, it is a real wavelet function instead of a general Shannon–Gabor wavelet which is a kind of quasi-wavelet. Next, by means of the Shannon–Cosine wavelet collocation method, the corresponding algebraic equation system of the fractional Fokker–Planck equation can be obtained. Approximate solutions of the fractional Fokker–Plank equations are compared with the exact solutions. These calculations illustrate that the accuracy of the Shannon–Cosine wavelet collocation solutions is quite high even using a small number of grid points.

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Skirvin, S. J., V. Fedun, and G. Verth. "I. The effect of symmetric and spatially varying equilibria and flow on MHD wave modes: slab geometry." Monthly Notices of the Royal Astronomical Society 504, no. 3 (2021): 4077–92. http://dx.doi.org/10.1093/mnras/stab1143.

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ABSTRACT Realistic theoretical models of magnetohydrodynamic wave propagation in the different solar magnetic configurations are required to explain observational results, allowing magnetoseismology to be conducted and provide more accurate information about local plasma properties. The numerical approach described in this paper allows a dispersion diagram to be obtained for any arbitrary symmetric magnetic slab model of solar atmospheric features. This proposed technique implements the shooting method to match necessary boundary conditions on continuity of displacement and total pressure of the waveguide. The algorithm also implements fundamental physical knowledge of the sausage and kink modes such that both can be investigated. The dispersion diagrams for a number of analytic cases that model magnetohydrodynamic waves in a magnetic slab were successfully reproduced. This work is then extended by considering density structuring modelled as a series of Gaussian profiles and a sinc(x) function. A further case study investigates properties of MHD wave modes in a coronal slab with a non-uniform background plasma flow, for which the governing equations are derived. It is found that the dispersive properties of slow body modes are more greatly altered than those of fast modes when any equilibrium inhomogeneity is increased, including background flow. The spatial structure of the eigenfunctions is also modified, introducing extra nodes and points of inflexion that may be of interest to observers.

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Kamel, Al-Khaled, and Abu-Irwaq Issam. "Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 5 (2019): 3720–31. https://doi.org/10.11591/ijece.v9i5.pp3720-3731.

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The present article is designed to supply two different numerical solutions for solv- ing Kuramoto-Sivashinsky equation. We have made an attempt to develop a numeri- cal solution via the use of Sinc-Galerkin method for Kuramoto-Sivashinsky equation, Sinc approximations to both derivatives and indefinite integrals reduce the solution to an explicit system of algebraic equations. The fixed point theory is used to prove the convergence of the proposed methods. For comparison purposes, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. In addition, we present numerical examples and comparisons to support the validity of these proposed methods.

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Mandelbrot, Benoit B. "Renormalization and fixed points in finance, since 1962." Physica A: Statistical Mechanics and its Applications 263, no. 1-4 (1999): 477–87. http://dx.doi.org/10.1016/s0378-4371(98)00520-2.

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Ouellette, Nadine, Magali Barbieri, and John R. Wilmoth. "Period-Based Mortality Change: Turning Points in Trends since 1950." Population and Development Review 40, no. 1 (2014): 77–106. http://dx.doi.org/10.1111/j.1728-4457.2014.00651.x.

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Neumaier, Paul. "Themenschwerpunkt: Scheiterpunkte / Points of Failure. Sind wir gescheitert? / Have we failed?" Themenzentrierte Interaktion 38, no. 2 (2024): 146–54. http://dx.doi.org/10.13109/tzin.2024.38.2.146.

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LECLAIR, ANDRÉ, and DENNIS NEMESCHANSKY. "AFFINE LIE ALGEBRA SYMMETRY OF SINE-GORDON THEORY AT REFLECTIONLESS POINTS." Modern Physics Letters A 11, no. 02 (1996): 139–46. http://dx.doi.org/10.1142/s0217732396000163.

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The quantum affine symmetry of the sine-Gordon theory at q2=1, which occurs at the reflectionless points, is studied. Conserved currents that correspond to the closure of simple root generators are considered, and shown to be local. We argue that they satisfy the [Formula: see text] algebra. Examples of these currents are explicitly constructed.

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Muscatello, Mariagrazia, Ndèye Mané Touré, Francesco Venturi, et al. "Vantage Points." TURBA 2, no. 2 (2023): 85–123. http://dx.doi.org/10.3167/turba.2023.020205.

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A distinctive trait of the Chilean art scene, its insular condition came about as a consequence of the 1973 coup d’état, which interrupted foreign relations for a long time. The situation is only now being reversed, with local artistic production still being restricted to a homegrown market and audiences. Within this national circuit of the arts, almost entirely centered in the city of Santiago, artistic work is mostly limited to the activity of graduates and faculty from metropolitan universities, such as the Universidad de Chile and the Universidad Católica. The trend is now being reversed thanks to recent social events, primarily the 2019 uprisings or the increased market value of lithium, which put Chile back at the center of the global geopolitical agenda. In addition, a shift in media attention toward the art of indigenous peoples, which peaked in 2022, with examples such as the Venice Biennale, has allowed artists like Cecilia Vicuña, active since the seventies, to enter the so-called star system of art.

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WANG, XING-YUAN, and FENG-DAN GE. "THE QUASI-SINE FIBONACCI HYPERBOLIC DYNAMIC SYSTEM." Fractals 18, no. 01 (2010): 45–51. http://dx.doi.org/10.1142/s0218348x10004725.

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This paper researches the dynamic behavior of a general form of the Fibonacci function, which is a quasi-sine Fibonacci function. It analyses the fixed points of the quasi-sine Fibonacci function on the real axis and the complex plane, and then constructs the Julia set of it using the escape-time method, discovering that the Julia set is fractal and it is on the x-axis symmetry. Using the conception of critical point, the quasi-sine Fibonacci function is generalized. Later the paper examines the dynamic behavior of the generalized quasi-sine Fibonacci function on critical points, and finds that the Mandelbrot set is also on the x-axis symmetry. Finally, it is discovered that there is a jumping phenomenon on the critical points.

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33

Benedetto, Giacomo. "Power, money and reversion points: the European Union's annual budgets since 2010." Journal of European Public Policy 24, no. 5 (2016): 633–52. http://dx.doi.org/10.1080/13501763.2016.1154589.

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Journal, Baghdad Science. "On Soft Turning Points." Baghdad Science Journal 15, no. 3 (2018): 352–60. http://dx.doi.org/10.21123/bsj.15.3.352-360.

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The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

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35

Abtahi, Mortaza, Zoran Kadelburg та Stojan Radenovic. "Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces". Applied General Topology 19, № 2 (2018): 189. http://dx.doi.org/10.4995/agt.2018.7409.

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<p>New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces.</p>

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36

Ji, Seungmuk, Ja-Yong Koo, and Taejin Lee. "Dissipative Hofstadter Model at the Magic Points and Critical Boundary Sine-Gordon Model." Journal of the Korean Physical Society 50, no. 11 (2007): 54. http://dx.doi.org/10.3938/jkps.50.54.

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Ellis, Frank. "Growing points in radiotherapy since 1930. The 65th Mackenzie Davidson Memorial Lecture 1984." British Journal of Radiology 60, no. 709 (1987): 51–68. http://dx.doi.org/10.1259/0007-1285-60-709-51.

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38

Hong, Chang-Zern. "Myofascial Trigger Points: Pathophysiology and Correlation with Acupuncture Points." Acupuncture in Medicine 18, no. 1 (2000): 41–47. http://dx.doi.org/10.1136/aim.18.1.41.

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A review is made of recent studies on myofascial trigger points (MTrP) and their mechanism is discussed. Clinical and basic science studies have shown that there are multiple MTrP loci in a MTrP region. A MTrP locus contains a sensory component (sensitive locus) and a motor component (active locus). A sensitive locus is a point from which tenderness or pain, referred pain, and local twitch response can be elicited by mechanical stimulation. Sensitive loci (probably sensitised nociceptors) are widely distributed in the whole muscle, but are concentrated in the endplate zone. An active locus is a site from which spontaneous electrical activity can be recorded. Active loci appear to be dysfunctional endplates since spontaneous electrical activity is essentially the same as the electrical activity reported by neurophysiologists as that recorded from an abnormal endplate. A MTrP is always found in a taut band which is histologically related to contraction knots caused by excessive release of acetylcholine in abnormal endplates. Both referred pain and local twitch response are mediated through spinal cord mechanisms, as demonstrated in both human and animal studies. The pathogenesis of MTrPs appears to be related to integration in the spinal cord of response to the disturbance of nerve endings and abnormal contractile mechanism at multiple dysfunctional endplates. There are many similarities between MTrPs and acupuncture points including their location and distribution, pain and referred pain patterns, local twitch responses (de qi), and possible spinal cord mechanism.

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Balamurugan, R., and Dr M. Prakash. "A Survey on Efficient Transmission and Routing for Improved Sink Point Streaming in MANET." Journal of Advanced Research in Dynamical and Control Systems 11, no. 12-SPECIAL ISSUE (2019): 1175–80. http://dx.doi.org/10.5373/jardcs/v11sp12/20193324.

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40

Eswara, A. T. "MHD Boundary Layers Due to a Point Sink with Temperature-Dependent Viscosity/Prandtl Number." International Journal of Modeling and Optimization 4, no. 5 (2014): 350–53. http://dx.doi.org/10.7763/ijmo.2014.v4.399.

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Htiti, Mohamed, Ismail Akharraz, and Abdelaziz Ahaitouf. "A novel one-dimensional chaotic map with improved sine map dynamics." International Journal of Electrical and Computer Engineering (IJECE) 15, no. 2 (2025): 2128–37. https://doi.org/10.11591/ijece.v15i2.pp2128-2137.

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These days, keeping information safe from people who should not have access to it is very important. Chaos maps are a critical component of encryption and security systems. The classical one-dimensional maps, such as logistic, sine, and tent, have many weaknesses. For example, these classical maps may exhibit chaotic behavior within the narrow range of the rate variable between 0 and 1and the small interval's rate variable. In recent years, several researchers have tried to overcome these problems. In this paper, we propose a new one-dimensional chaotic map that improves the sine map. We introduce an additional parameter and modify the mathematical structure to enhance the chaotic behavior and expand the interval's rate variable. We evaluate the effectiveness of our map using specific tests, including fixed points and stability analysis, Lyapunov exponent analysis, diagram bifurcation, sensitivity to initial conditions, the cobweb diagram, sample entropy and the 0-1 test.

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42

Miles, Bertie W. J., and Robert G. Bingham. "Progressive unanchoring of Antarctic ice shelves since 1973." Nature 626, no. 8000 (2024): 785–91. http://dx.doi.org/10.1038/s41586-024-07049-0.

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AbstractMass loss of the Antarctic Ice Sheet has been driven primarily by the thinning of the floating ice shelves that fringe the ice sheet1, reducing their buttressing potential and causing land ice to accelerate into the ocean2. Observations of ice-shelf thickness change by satellite altimetry stretch back only to 1992 (refs. 1,3–5) and previous information about thinning remains unquantified. However, extending the record of ice-shelf thickness change is possible by proxy, by measuring the change in area of the surface expression of pinning points—local bathymetric highs on which ice shelves are anchored6. Here we measure pinning-point change over three epochs spanning the periods 1973–1989, 1989–2000 and 2000−2022, and thus by proxy infer changes to ice-shelf thickness back to 1973–1989. We show that only small localized pockets of ice shelves were thinning between 1973 and 1989, located primarily in the Amundsen Sea Embayment and the Wilkes Land coastline. Ice-shelf thinning spreads rapidly into the 1990s and 2000s and is best characterized by the proportion of pinning points reducing in extent. Only 15% of pinning points reduced from 1973 to 1989, before increasing to 25% from 1989 to 2000 and 37% from 2000 to 2022. A continuation of this trend would further reduce the buttressing potential of ice shelves, enhancing ice discharge and accelerating the contribution of Antarctica to sea-level rise.

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KIM, Jeong-Gyoo. "An Arc-Sine Law for Last Hitting Points in the Two-Parameter Wiener Space." Mathematics 7, no. 11 (2019): 1131. http://dx.doi.org/10.3390/math7111131.

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We develop the two-parameter version of an arc-sine law for a last hitting time. The existing arc-sine laws are about a stochastic process X t with one parameter t. If there is another varying key factor of an event described by a process, then we need to consider another parameter besides t. That is, we need a system of random variables with two parameters, say X s , t , which is far more complex than one-parameter processes. In this paper we challenge to develop such an idea, and provide the two-parameter version of an arc-sine law for a last hitting time. An arc-sine law for a two-parameter process is hardly found in literature. We use the properties of the two-parameter Wiener process for our development. Our result shows that the probability of last hitting points in the two-parameter Wiener space turns out to be arcsine-distributed. One can use our results to predict an event happened in a system of random variables with two parameters, which is not available among existing arc-sine laws for one parameter processes.

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44

Fieldseth, Melanie. "Turning Points and Conflicting Interests." Nordic Theatre Studies 33, no. 1 (2022): 43–57. http://dx.doi.org/10.7146/nts.v33i1.131991.

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Teaterhuset Avant Garden (TAG) was a theatre in Trondheim that co-produced and presented the work of independent performing artists and groups fromNorway and abroad. By taking a closer look at events between 1993 and 2003, this article situates TAG within broader aesthetic, organizational, and politicalcontexts and analyses the impact of these events on visions for the theatre’s future. The article is based on archival research for a forthcoming book onTAG that deals with the period 1984–2018. In 2019, TAG changed its name to Rosendal Teater in honour of the historic building where it has since relocated.

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45

Fieldseth, Melanie. "Turning Points and Conflicting Interests." Nordic Theatre Studies 33, no. 1 (2022): 43–57. http://dx.doi.org/10.7146/nts.v33i1.131991.

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Teaterhuset Avant Garden (TAG) was a theatre in Trondheim that co-produced and presented the work of independent performing artists and groups fromNorway and abroad. By taking a closer look at events between 1993 and 2003, this article situates TAG within broader aesthetic, organizational, and politicalcontexts and analyses the impact of these events on visions for the theatre’s future. The article is based on archival research for a forthcoming book onTAG that deals with the period 1984–2018. In 2019, TAG changed its name to Rosendal Teater in honour of the historic building where it has since relocated.

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46

Fieldseth, Melanie. "Turning Points and Conflicting Interests." Nordic Theatre Studies 33, no. 1 (2022): 43–57. http://dx.doi.org/10.7146/nts.v33i1.131991.

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Teaterhuset Avant Garden (TAG) was a theatre in Trondheim that co-produced and presented the work of independent performing artists and groups fromNorway and abroad. By taking a closer look at events between 1993 and 2003, this article situates TAG within broader aesthetic, organizational, and politicalcontexts and analyses the impact of these events on visions for the theatre’s future. The article is based on archival research for a forthcoming book onTAG that deals with the period 1984–2018. In 2019, TAG changed its name to Rosendal Teater in honour of the historic building where it has since relocated.

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47

Rashid, Asif. "How policing has changed since COVID-19." Journal of Intelligence, Conflict, and Warfare 3, no. 3 (2021): 88–90. http://dx.doi.org/10.21810/jicw.v3i3.2753.

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Superintendent Asif Rashid of Calgary Police discussed policing changes since COVID-19 on November 26, 2020 at the 2020 CASIS West Coast Security Conference. The presentation was followed by a question and answer period with the other speakers of the panel. The key points discussed were how policing was changed to adapt to the challenges of COVID-19, emergency management systems, and technological issues.

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48

Pérez, Isidro A., Mª Ángeles García, Mª Luisa Sánchez, Nuria Pardo, and Beatriz Fernández-Duque. "Key Points in Air Pollution Meteorology." International Journal of Environmental Research and Public Health 17, no. 22 (2020): 8349. http://dx.doi.org/10.3390/ijerph17228349.

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Although emissions have a direct impact on air pollution, meteorological processes may influence inmission concentration, with the only way to control air pollution being through the rates emitted. This paper presents the close relationship between air pollution and meteorology following the scales of atmospheric motion. In macroscale, this review focuses on the synoptic pattern, since certain weather types are related to pollution episodes, with the determination of these weather types being the key point of these studies. The contrasting contribution of cold fronts is also presented, whilst mathematical models are seen to increase the analysis possibilities of pollution transport. In mesoscale, land–sea and mountain–valley breezes may reinforce certain pollution episodes, and recirculation processes are sometimes favoured by orographic features. The urban heat island is also considered, since the formation of mesovortices determines the entry of pollutants into the city. At the microscale, the influence of the boundary layer height and its evolution are evaluated; in particular, the contribution of the low-level jet to pollutant transport and dispersion. Local meteorological variables have a major influence on calculations with the Gaussian plume model, whilst some eddies are features exclusive to urban environments. Finally, the impact of air pollution on meteorology is briefly commented on.

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Zhang, Xurui. "Development of RSA and some attack points." Theoretical and Natural Science 11, no. 1 (2023): 1–6. http://dx.doi.org/10.54254/2753-8818/11/20230367.

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Currently, the relatively popular public key encryption is RSA. It was officially launched in 1978 and given their initials as a name. Different encryption and decryption keys are used in the RSA public-key cryptosystem. Deriving decryption keys from known encryption keys is computationally difficult. Rsa has emerged in various forms since its development. Since the development of RSA, there have been various forms, which means there are various loopholes. Next, we will summarize several interesting attack methods of rsa. It will involve continued fractions and CRT and so on. Through this paper, one can learn a series of knowledge about rsa. As a classic asymmetric password, the value of rsa's existence is relatively high, and exploring its value is something that every password learner should experience. Through this article, one will learn about the most basic attack methods of rsa.

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Jaume, Andrés. "PERSPECTIVES, POINTS OF VIEW, AND FRAMES. ON THE POSSIBILITY OF EVALUATING POINTS OF VIEW." Análisis. Revista de investigación filosófica 11, no. 2 (2024): 317–23. https://doi.org/10.26754/ojs_arif/arif.2024211340.

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This collaboration addresses the difference between the concepts of perspective, point of view, and conceptual framework. This distinction allows us to avoid the problem of circularity in philosophical perspectivism while preventing us from falling into relativism. The basic notion is perspective, and points of view are understood as ways of conceptualizing certain aspects of reality. Conceptual frameworks are seen as systems of points of view that can have a greater or lesser scope. Finally, the concept of personal fulfillment is proposed as the ultimate criterion for determining how it is possible to improve one's point of view, since it is assumed that not all points of view have the same value, against skeptical assumptions, and that consequently, there is no room for vicious circularity in the philosophical perspectivism upheld here.

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Journal articles on the topic 'Sinc points'

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