In the present work a statistical investigation of the spatial distribution of longitudinal coordinates of sunspot data has been carried out. For the analysis the maximal area of umbra plus penumbra of sunspot groups has been taken into account. Spatial distributions of longitudinal coordinates of sunspot data are obtained in diierent coordinate systems (e.g. Carrington, equatorial and diierent...

Because of different behavior of reservoir water and dam material, the determination of hydrodynamic pressure during earthquake is very complicated. Thus, different formulations have been presented for modeling of the dam reservoir system under dynamic loading such as earthquake. These formulations can be categorized into two general groups, which are Lagrangian and Eulerian, each having advant...

This is the third part of the five-part saga on the umbral transfermatrix method, based on Gian-Carlo Rota’s seminal notion of the umbra. In this article we describe the Maple package ZOO that for any specific k, automatically constructs an umbral scheme for enumerating “k-board” lattice animals (polyominoes) on the two-dimensional square lattice. Such umbral schemes enable counting these impor...

Efficient implementation of morphological operations requires the decomposition of structuring elements into the dilation of smaller structuring elements. Zhuang and Haralick (1986) presented a search algorithm to find optimal decompositions of structuring elements in binary morphology. We use the concepts of Top of a set and Umbra of a surface to extend this algorithm to find an optimal decomp...

We report spectropolarimetric observations of a supersonic downflow impacting the lower atmosphere within large sunspot umbra. This work is an extension Schad et al. using acquired in He i 10830 Å triplet by Facility Infrared Spectropolarimeter. Downflowing material accelerating along cooled coronal loop reaches peak speeds near 200 km s−1 and exhibits both high speed emission absorption umbra,...

By adding a proper term to the Lagrangian density of a real non-linear KG system with a proposed non-topological unstable solitary wave solution, its stability guaranteed appreciably. This additional term in the new modified Lagrangian density behaves like a strong internal force which stands against any arbitrary small deformation in the proposed non-topological solitary wave solution.