In this work, we present the notion of sp[γ,γ^(* ) ]-open set,  sp[γ,γ^(* ) ]-closed, and sp[γ,γ^(* ) ]-closure such that several properties are obtained. By using this concept, we define a new type of spaces named sp[γ,γ^(* ) ]-compact space.

High Q-factor based on absorption can be achieved by tuning (the reflection and the transition percentage). In this work, the simple design and simulated in S-band have been investigated. The simulation results of G-shape resonator are shown triple band of absorption peaks 60%, 91.5%, and 70.3%) at resonance frequency 2.7 GHz, 3.26 GHz, and 4.05 GHz respectively. The results exhibited very high of the Q-factor ( 271 ) at resonance frequency ( 3.26 GHz ).  The high Q-factor can be used to enhance the sensor sensing, narrowband band filter and  image sensing.

Most recent studies have focused on using modern intelligent techniques spatially, such as those
developed in the Intruder Detection Module (IDS). Such techniques have been built based on modern
artificial intelligence-based modules. Those modules act like a human brain. Thus, they should have had the
ability to learn and recognize what they had learned. The importance of developing such systems came after
the requests of customers and establishments to preserve their properties and avoid intruders’ damage. This
would be provided by an intelligent module that ensures the correct alarm. Thus, an interior visual intruder
detection module depending on Multi-Connect Architecture Associative Memory (MCA)

      This paper intends to initiate a new type of generalized closed set in topological space with the theoretical application of generalized topological space. This newly defined set is a weaker form than the -closed set as well as -closed set. Some phenomenal characterizations and results of newly defined sets are inculcated in a proper manner. The characteristics of normal spaces and regular spaces are achieved in the light of the generalized pre-regular closed set.

    The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then Ais called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

      The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then A is called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.