This set of notes will try to set down in one coherent place, a general set of equations for calculating changes of major element, reactive trace element and U-series nuclides in an open system. Given the continuous form of the equations we will also deal with scaling and discrete forms using Semi-Lagrangian advection schemes. The key to these derivations will be using general conservation of m...

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

Let (X, z) be a topological space, and (Y, d) a metric space. A mapping F: X -+ 2’ which associates with every x E X a non-empty subset F(x) OF Y is said to be lower semi-continuous (I.s.c.) (respectively, upper semi-continuous (u.s.c.)) if, for each open set % in Y, the set (X E X: F(x) n %f # @ > (respectively, the set (X E X: F(x) c @ )) is open in X A mapping f: X-a Y is a selection for F i...

A set has local scaling if in a neighborhood of a point the structure of the set can be mapped onto a finer scale structure of the set. These scaling transformations are compact sets of locally affine contractions (that is, contractions with uniformly α-Hölder continuous derivatives). In this setting, without the open set condition or any other assumption on the spacing of these contractions, w...

For set-valued information systems, there are many original dot-based approximation models based on tolerance relations and other developed relations. Because of the lack efficient algorithms, they not to accommodate bigger table. Therefore, it is a real challenge how efficiently calculate high-quality set in systems. To address challenge, we propose reliable operators semi-monolayer covering f...