We examine the Seidel aberrations of thin spherical lenses composed of media with refractive index not restricted to be positive. We find that consideration of this expanded parameter space allows for the reduction or elimination of more aberrations than is possible with only positive index media. In particular, we find that spherical lenses possessing real aplanatic focal points are possible o...

Abstract. After formulating the design problem for Resampling Kernels used in Magnetic Resonance Spiral Image Reconstruction, we show that an iterative Gauss-Seidel-type interior-point optimization method is suitable (fast and light-weight) for embedded uses. In contrast to previous practice, we directly optimize a computationally efficient, piecewise-linear kernel rather than an analytic funct...

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New (NSGS), and Parametric (PSGS) methods for solving linear system Ax = b are considered. is precondition type I + S. Convergence properties analyzed standard procedures a numerical experiment undertaken to compare efficiency matrix. Algorithms prepared. MATLAB software used checking computational itera...

In this paper an estimator for speech enhancement based on Laplacian Mixture Model has been proposed. The proposed method, estimates the complex DFT coefficients of clean speech from noisy speech using the MMSE  estimator, when the clean speech DFT coefficients are supposed mixture of Laplacians and the DFT coefficients of  noise are assumed zero-mean Gaussian distribution. Furthermore, the MMS...

In this paper, we estimate the magnetic Laplacian energy norm in appropriate planar domains under a weak regularity hypothesis on field. Our main contribution is an averaging estimate, valid small cells, allowing us to pass from non-uniform uniform fields. As matter of application, derive new upper and lower bounds lowest eigenvalue Dirichlet which match regime large field intensity. Furthermor...

We study the limiting behavior of solutions to boundary value nonlinear problems involving fractional Laplacian order 2s when parameter s tends zero. In particular, we show that least-energy converge (up a subsequence) nontrivial nonnegative solution problem in terms logarithmic Laplacian, i.e. pseudodifferential operator with Fourier symbol \(\ln (|\xi |^2)\). These results are motivated by so...

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive ...

In the paper, we advance a numerical technique for enclosing generalized AE-solution sets to interval linear systems. The main result of the paper is an extension of the well-known interval Gauss-Seidel method to the problems of outer estimation of these generalized solution sets. We give a theoretical study of the new method, prove an optimality property for the generalized interval Gauss-Seid...

Experiments that discuss influence of noise to H. Seidel and H. Herzel dynamics model of human cardiovascular system are presented. Noise is introduced by considering stochastic delays in response to the sympathetic system. It appears that in the presence of the noise 10 s heart rate oscillations connected with Mayer waves are preserved. Moreover the heart rate becomes approximately normally di...