Suppose that  is a finite group and  is a non-empty subset of  such that  and . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper, we introduce the generalized Cayley graph denoted by  that  is a graph with vertex set consists of all column matrices  which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and . In this paper, we clarify some basic properties of the new graph and assign the structure of  when  is complete graph , complete bipartite graph  and complete

    In this paper, we prove some coincidence and common fixed point theorems for a pair of discontinuous weakly compatible self mappings satisfying generalized contractive condition in the setting of Cone-b- metric space under assumption that the Cone which is used is nonnormal. Our results are generalizations of some recent results.

     In this paper, we introduce new definitions of the - spaces  namely the    - spaces  Here,  and  are natural numbers that are not necessarily equal, such that . The space  refers to the n-dimensional Euclidean space,  refers to the quaternions set and  refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the  spaces  have never been introduced in this way before.

Discrete   logarithms  are applied      in many    cryptographic problems  . For instance ,   in public   key .  and for construction of sets with disti nct sums of  k-clcments.  The   purpose o r  this   paper

is  to  modify  the  method ol' informationl1·iding  using        discrete logarithms  , introduce new properties of St - sets ,   uscdthe direct product   of    groups   to construct  cyclic group and finally, present modified   method   for   knapsack &

Abstract. Hassan FM, Mahdi WM, Al-Haideri HH, Kamil DW. 2022. Identification of new species record of Cyanophyceae in Diyala River, Iraq based on 16S rRNA sequence data. Biodiversitas 23: 5239-5246. The biodiversity and water quality of the Diyala River require screening water in terms of biological contamination, because it is the only water source in Diyala City and is used for many purposes. This study aimed to identify a new species record of Cynaophyceae and emphasize the importance of using molecular methods beside classic morphological approaches, particularly in the water-shrinkage-aqua system. Five different sites along Diyala River were selected for Cyanophyceae identification. Morphological examination and 16S rRNA sequen

     In this work,  we presented a study of the structural formula for a new series of complexes with Ag(I), Cu(II), Zn(II), and Cd(II) derived from the guanine azo dye ligand 2-amino-8-((3-hydroxyphenyl)diazinyl)-1,7-dihydro-6H-purin-6-one (HAG), which is investigated using various physicochemical analyses, spectroscopic techniques (FT-IR, U.V-VIS, and ¹H NMR), thermogravimetric analysis (TGA). In addition, elemental analyses, magnetic susceptibility, and molar conductance measurements were all stabilized. As well as the mole ratio, stability constant, and Gibbs free energy were studied for all complexes, where they showed high stability and spontaneous synthesis. The Cu(II) complex was suggested to have octahedral stere

One of the most popular and legally recognized behavioral biometrics is the individual's signature, which is used for verification and identification in many different industries, including business, law, and finance. The purpose of the signature verification method is to distinguish genuine from forged signatures, a task complicated by cultural and personal variances. Analysis, comparison, and evaluation of handwriting features are performed in forensic handwriting analysis to establish whether or not the writing was produced by a known writer. In contrast to other languages, Arabic makes use of diacritics, ligatures, and overlaps that are unique to it. Due to the absence of dynamic information in the writing of Arabic signatures,

         Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.