Abstract In mathematics, a common approach to solving new problem is break down the into sub-problems that you know how solve and then try glue pieces together yield solution of problem. This also very useful in software development; well-tested can be glued order obtain solutions wider class problems. Operator splitting technique illustrates this principle well. Rather complex equations broken...

Summary . In this article we further develop field theory in Mizar [1], [2]: prove existence and uniqueness of splitting fields. We define the a polynomial p ∈ F [ X ] as smallest extension , which splits into linear factors. From follows, that for E have = ( A ) where is set ’s roots. Splitting fields are unique, however, only up to isomorphisms; be more precise -isomorphims i.e. isomorphisms ...

Splitting is a conventional process in most of Indian languages according to their grammar rules. It is called ‘pada vicchEdanam’ (a Sanskrit term for word splitting) and is widely used by most of the Indian languages. Splitting plays a key role in Machine Translation (MT) particularly when the source language (SL) is an Indian language. Though this splitting may not succeed completely in extra...

Measurements of seismic anisotropy constitute a very important tool for examining patterns of flow and mineral properties in the Earth’s mantle. A popular strategy for gaining insight into upper mantle processes is to examine the splitting of SK(K)S phases and interpret them in terms of upper mantle anisotropy and deformation; in such studies, any contribution to splitting from anisotropy in th...