In this research, the Boiti–Leon–Pempinelli (BLP) system was used to understand the physical meaning of exact and solitary traveling wave solutions. To establish modern exact results, considered. In addition, the results obtained were compared with those obtained by using other existing methods, such as the standard hyperbolic tanh function method, and the stability analysis for the results was discussed.

May R.M. gave the example of the family of cubic maps of the interval . Rogers T. D. extends the analysis of May beyond that region . “ In this paper we are trying to introduce comprehensive study of the cubic family which defined in the form: The fixed points of the family are determined and described according to the values of the parameter  . Dynamical and chaotic behaviours of the family  discussed according to different definitions of chaos and via conjugacy .   http://dx.doi.org/10.25130/tjps.24.2019.058

The current study deals with the dynamical behavior of three cubic functions in the complex plane. Critical and fixed points of all of them were studied . Properties of every point were studied and the nature of them was determined if it is either attracting or repelling. First function  such that have two critical points  and three fixed points  such that is attracting when  is origin point As shown in figure (2).And  are attracting when  is the region specified by open disc  shown in figure (1.(c)).Second function  such that have two critical points   and three fixed points such that  is attracting when  and that its path is to the origin point as shown in figure (4).And  are attractive when  represents the open disc shown in the figure (3.(c)).Third function  such that  have one critical point  and three fixed points  is attracting that is path is the origin point and  are repelling as shown in figure (5). And all 2-cycles of  are repelling and unstable .

The Transmuted Topp Leone Flexible Weibull distribution was developed in this paper using the Transmuted Topp Leone family of distributions and its basic statistical properties were established. Estimation of model parameters was considered using the maximum likelihood estimation (MLE) method and three real life applications were provided. The TTLFW distribution is a promising model as its performance relative to other compounds probability models like the Exponentiated Flexible Weibull, Weibull Flexible Weibull, Kumaraswamy Flexible Weibull, Beta Flexible Weibull, Gamma Flexible Weibull, and Exponentiated Generalized Flexible Weibull distributions is quite credible.

The main goal of this paper is to use the concept _ open sets to present new classes of separation axioms in _topological spaces. Those new classes are _spaces, =0,1,2. We have studied some basic properties of these spaces. We also discussed the relationship between _spaces and Nano separation axioms spaces), =0,1,2. Furthermore the paper deals with the relationship between the separation axioms throughout kernel set associated with the closed set which used to prove some theorems related to it. The hereditary and topological properties were also discussed.