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.

            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  .

A transdermal drug delivery system (TDDS) is characterized by the application of medications onto the skin's surface to deliver drugs at a controlled and predefined rate through the skin. Spanlastics, an elastic nanovesicle capable of transporting various pharmacological substances, shows promise as a drug delivery carrier. It offers numerous advantages over traditional vesicular systems applied topically, including enhanced stability, flexibility in penetration, and improved targeting capabilities. This study aims to develop meloxicam (MX)-loaded spanlastics gel as skin delivery carriers and to look into the effects of formulation factors like Tween80, Brij 35, and carbopol concentration on the properties of spanlastics gel, like pH, drug

     New chelating ligand derived from triazole and its complexes with metal ions Rhodium, Platinum and Gold were synthesized. Through a copper (I)-catalyzed click reaction, the ligand produced 1,3-dipolar cycloaddition between 2,6-bis((prop-2-yn-1-yloxy) methyl) pyridine and 1-azidododecane. All structures of these new compounds were rigorously characterized in the solid state using spectroscopic techniques like: ¹HNMR, ¹³CNMR, Uv-Vis, FTIR, metal and elemental analyses, magnetic susceptibility and conductivity measurements at room temperature, it was found that the ligand acts as a penta and tetradentate chelate through N₃O₂, N₂O₂, and the geometry of the new complex

     New chelating ligand derived from triazole and its complexes with metal ions Rhodium, Platinum and Gold were synthesized. Through a copper (I)-catalyzed click reaction, the ligand produced 1,3-dipolar cycloaddition between 2,6-bis((prop-2-yn-1-yloxy) methyl) pyridine and 1-azidododecane. All structures of these new compounds were rigorously characterized in the solid state using spectroscopic techniques like: 1HNMR, 13CNMR, Uv-Vis, FTIR, metal and elemental analyses, magnetic susceptibility and conductivity measurements at room temperature, it was found that the ligand acts as a penta and tetradentate chelate through N3O2, N2O2, and the geometry of the new complexes are identified as octahedral for (Rh & Pt) complexes a

In this study, chalcones were synthesis by condensing 2-acetylpyridine with aromatic aldehyde derivatives in dilute ethanolic potassium hydroxide solution at room temperature according to Claisen-Schmidt condensation. After that, new heterocyclic derivatives such as Oxazine, Thiazine and Pyrazol were synthesis by reaction between chalcones with urea, thiourea and hydrazine hydrate respectively scheme 1. All these compounds wrer characterization by FTIR, 1H-NMR spectroscopy and elemental analysis.

In this present work, [4,4`-(biphenyl-4,4`-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-1-ylidene)bis(2-methoxyphenl)(A1),4,4`-(biphenyl-4,4`-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-1-ylidene)diphenol(A2),1,1`-(biphenyl-4,4`-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-1-ylidene) dinaphthalen-2-ol (A3)]C.S was prepared in 3.5% NaCl. Corrosion prevention at (293-323) K has been studied by using electrochemical measurements. It shows that the utilized inhibitors are of mixed type based on the polarization curves. The results indicated that the inhibition efficiency changes were used with a change according to the functional groups on the benzene ring and through the electrochemical technique. Temperature increases with corrosion current