This work includes design, implementation and testing of a microcontroller – based spectrum analyzer system. Both hardware and software structures are built to verify the main functions that are required by such system. Their design utilizes the permissible and available tools to achieve the main functions of the system in such a way to be modularly permitting any adaptation for a specific changing in the application environment. The analysis technique, mainly, depends on the Fourier analysis based methods of spectral analysis with the necessary required preconditioning processes. The software required for waveform analysis has been prepared. The spectrum of the waveform has been displayed, and the instrument accuracy has been checked.

The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

An environmentally begnin second derivative spectrometric approach was developed for the estimation of the dissociation constants pKa(s) of metformin, a common anti-diabetic drug.  The ultraviolet spectra of the aqueous solution of metformin were measured at different acidities, then the second derivative of each spectrum was graphed. The overlaid second derivative graphs exhibited two isobestic points at 225.5 nm and 244 nm pointing out to the presence of two dissociation constants for metformin pKa1 and pKa2, respectively. The method was validated by evaluating the reproducibility of the acquired results by comparing the estimated values of the dissociation constants of two different strategies that show excellent matching. As we

Research summary

Praise be to God, and prayers and peace be upon our master Muhammad, his family and companions until the Day of Judgment.

As for after:

It is the right of every nation to take care of its scientific heritage, and to reveal its human civilizational impact, and the Arabs are the richest nations in heritage, as they had in every period of time a sign and pride, the Arabs fulfilled their duty towards humanity, and they carried out a large part of their scientific activity towards humanity.

Therefore, highlighting some of the scientific aspects of the civilized activity of the Arabs, and removing some of the illusions spread by some malicious people, is a human duty before it is a national duty.

We define and study new ideas of fibrewise topological space on D namely fibrewise multi-topological space on D. We also submit the relevance of fibrewise closed and open topological space on D. Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space on D. Furthermore, we propose and prove a number of statements about these ideas.

Fibrewise topological spaces theory is a relatively new branch of mathematics, less than three decades old, arisen from algebraic topology. It is a highly useful tool and played a pivotal role in homotopy theory. Fibrewise topological spaces theory has a broad range of applications in many sorts of mathematical study such as Lie groups, differential geometry and dynamical systems theory. Moreover, one of the main objects, which is considered in fibrewise topological spaces theory is connectedness. In this regard, we of the present study introduce the concept of connected fibrewise topological spaces and study their main results.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near topological spaces over B. Also, we introduce the concepts of fibrewise near closed and near open topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

Abstract. One of the fibrewise micro-topological space is one in which the topology is decided through a group of fibre bundles, in comparison to the usual case in normal, fibrewise topological space. The micro-topological spaces draw power from their ability to be used in descriptions of a wide range of mathematical objects. These can be used to describe the topology of a manifold or even the topology of a group. Apart from easy manipulation, the fibrewise micro-topological spaces yield various mathematical applications, but the one being mentioned here is the possibility for geometric investigation of space or group structure. In this essay, we shall explain what fibrewise micro-topological spaces are, indicate why they are useful in math

In this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.