In this paper, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

Let M be a n-dimensional manifold. A C1- map f : M  M is called transversal if for all m N the graph of fm intersect transversally the diagonal of MM at each point (x,x) such that x is fixed point of fm. We study the minimal set of periods of f(M per (f)), where M has the same homology of the complex projective space and the real projective space. For maps of degree one we study the more general case of (M per (f)) for the class of continuous self-maps, where M has the same homology of the n-dimensional sphere.

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

   The main aim of this paper is to use the notion  which was introduced in [1], to offered new classes of separation axioms in ideal spaces. So, we offered new type of notions of convergence in ideal spaces via the set. Relations among several types of separation axioms that offered were explained.

     This research develops a new method based on spectral indices and random forest classifier to detect paddy rice areas and then assess their distributions regarding to urban areas. The classification will be conducted on Landsat OLI images and Landsat OLI/Sentinel 1 SAR data. Consequently, developing a new spectral index by analyzing the relative importance of Landsat bands will be calculated by the random forest. The new spectral index has improved depending on the most three important bands, then two additional indices including the normalized difference vegetation index (NDVI), and standardized difference built-up index (NDBI) have been used to extract paddy rice fields from the data. Several experiments being

    The Ozone Monitoring Instrument (OMI) measures the reflected solar radiation in the ultraviolet and visible part in the spectral range that is between 270 and 500 nm, using two channels with a spectral resolution of about 0.5 nm. Ground-level tropospheric ozone is one of the air pollutants of most concern. In the troposphere, near the Earth's surface, human activities lead to ozone concentrations several times higher than the natural background level. To evaluate the ozone distribution over Iraq, the ozone data from OMI were analyzed using geostatistical techniques. Theoretical spherical models provided the best fit for all monthly experimental variograms. The parameters of these variograms (sill, range and nugget) wer

     Let R be an associative ring. The essential purpose of the present paper is to introduce the concept of generalized commuting mapping of R. Let U be a non-empty subset of R, a mapping   : R  R is called a generalized commuting mapping on U if there exist a mapping :R R such that =0, holds for all U. Some results concerning the new concept are presented.