Quasigroups are algebraic structures closely related to Latin squares which have many different applications. There are several classifications of quasigroups based on their algebraic properties. In this paper we propose another classification based on the properties of strings obtained by specific quasigroup transformations. More precisely, in our research we identified some quasigroup transfo...

In this paper, we investigate under what circumstances the Laplace–Beltrami operator on a pseudo-Riemannian manifold can be written as a sum of squares of vector fields, as is naturally the case in Euclidean space. We show that such an expression exists globally on one-dimensional manifolds and can be found at least locally on any analytic pseudo-Riemannian manifold of dimension greater than tw...

In the Echo State Networks (ESN) and, more generally, Reservoir Computing paradigms (a recent approach to recurrent neural networks), linear readout weights, i.e., linear output weights, are the only ones actually learned under training. The standard approach for this is SVD–based pseudo–inverse linear regression. Here it will be compared with two well known on–line filters, Least Minimum Squar...

in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

An approach to correct the baseline handwritten word skew in the image of bank check dates is presented in this article. The main goal of such approach is to reduce the use of empirical thresholds. The weighted least squares approach is used on the pseudo-convex hull obtained from the mathematical morphology.

Tone mapping is used to compress the dynamic range of image data without distortion. To HDR images and prevent halo artifacts, a tone method proposed based on least squares method. Our first uses weights for estimation illumination, detail layer obtained by Retinex model. Then, global function with parameter range, fitting histogram equalization. Finally, illumination are fused obtain LDR image...

When fitting models to data containing multiple structures, such as when fitting surface patches to data taken from a neighborhood that includes a range discontinuity, robust estimators must tolerate both gross outliers and pseudo outliers. Pseudo outliers are outliers to the structure of interest, but inliers to a different structure. They differ from gross outliers because of their coherence....

In this paper we quantify the impact of model mis-specification on the properties of parameter estimators applied to fractionally integrated processes. We demonstrate the asymptotic equivalence of four alternative parametric methods: frequency domain maximum likelihood, Whittle estimation, time domain maximum likelihood and conditional sum of squares. We show that all four estimators converge t...

Stacking operators are widely used in seismic imaging and seismic data processing. Examples include Kirchhoff datuming, migration, offset continuation, DMO, and velocity transform. Two primary approaches exist for inverting such operators. The first approach is iterative least-squares optimization, which involves the construction of the adjoint operator. The second approach is asymptotic invers...

soil conservation service (scs) adjusted the kostiakovs infiltration model by adding a constant coefficient, for improvement of estimation. the improved model has three constant parameters, which are difficult to calculate. so scs has taken the third constant parameter as equal to 0.65-0.7 cm to simplify the estimation. this parameter varies in different soil and often outranges the scs estimat...