In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.

For structural concrete members that may expose to serious earthquake, overload or accident impact, the design of ductility must be given the same importance as the flexural strength. The aim of this investigation is to study the change in ductility of structural concrete flexural members during their exposure to limited cycles of repeated loading. Twenty full-scale beam specimens have been fabricated in to two identical groups; each group consisted of ten specimens. The first group was tested under monotonic static loading to failure and regarded as control beams, while the specimens of the second group were subjected to ten cycles of repeated loading with constant load interval, which ranged between 40% and 60% of ultimate load. S

For structural concrete members that may expose to serious earthquake, overload or accident impact, the design of ductility must be given the same importance as the flexural strength. The aim of this investigation is to study the change in ductility of structural concrete flexural members during their exposure to limited cycles of repeated loading. Twenty full-scale beam specimens have been fabricated in to two identical groups; each group consisted of ten specimens. The first group was tested under monotonic static loading to failure and regarded as control beams, while the specimens of the second group were subjected to ten cycles of repeated loading with constant load interval, which ranged between 40% and 60% of ultimate load. S

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

In this work, a comparative analysis for the behavior and pattern of the variations of the IF2 and T Ionospheric indices was conducted for the minimum and maximum years of solar cycles 23 and 24. Also, the correlative relationship between the two ionospheric indices was examined for the seasonal periods spanning from August 1996 to November 2008 for solar cycle 23 and from December 2008 to November 2019 for solar cycle 24. Statistical calculations were performed to compare predicted values with observed values for the selected indices during the tested timeframes. The study's findings revealed that the behavior of the examined indices exhibited almost similar variations throughout the studied timeframe. The seasonal variations were

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

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.