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.

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.

            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  .

Background: Coated aesthetic archwires are currently the existing solutions for the esthetic problem, but the color of these archwires tends to change overtime. This study was aimed to evaluate the color stability of different types of esthetic archwires from four different companies at different time periods after immersion of two different staining drinks which are tea and Pepsi cola. Materials and methods: 48 specimens were prepared, each specimen contains 10 aesthetic archwires; and were divided according to type of solution into two groups: A (tea) &B (Pepsi cola); each group contained 24 specimens (12 specimens were immersed in the staining solution as 4 specimens for each time intervals and 12 specimens were immersed in distilled wa

Background: pregnancy as a systemic condition causes changes in the functioning of human body as a whole and specifically in the oral cavity and it also is considered as a stressful condition. These changes may favor the increase of oxidative stress. Aim: The aim of this study was to estimate the level of marker of oxidative stress (malondialdehyde) and antioxidant (uric acid) in saliva of pregnant compared to non-pregnant women and to assess the gingival health condition in both groups. Additionally, unstimulated salivary flow rate was determined in both groups. Subjects, materials and methods: The study group consisted of sixty pregnant women, they were divided into three equal groups according to trimester (20 pregnant women for each

Background: One of the drawbacks of vital teeth bleaching is color stability. The aim of the present study was to evaluate the effects of tea and tomato sauce on the color stability of bleached enamel in association with the application of MI Paste Plus (CPP-ACPF). Materials and Methods: Sixty enamel samples were bleached with 10% carbamide peroxide for two weeks then divided into three groups (A, B and C) of 20 samples each. After bleaching, the samples of each group were subdivided into two subgroups (n=10). While subgroups A1, B1 and C1 were kept in distilled water, A2, B2, and C2 were treated with MI Paste Plus. Then, the samples were immersed in different solutions as follow: A1 and A2 in distilled water (control); B1 and B2 in black

Salicylaldehyde was react with 4-amino-2,3-dimethyl-1-phenyl-3-Pyrazoline-5-on to produce the novel Schiff base ligand 2,3-dimethyl-1-phenyl-4-salicylidene-3-pyrazoline-5-on (HL). A new complexes of VO(II), Cr(Ш), Zn(II), Cd(II), Hg(II) and UO2(II) with mixed ligands of bipyridyl and new shiff base ( 2,3-dimethyl-1-phenyl-4-salicylidene-3-pyrazoline-5-on) (HL) were prepared . All prepared compounds were identified by atomic absorption, FT.IR , UV-Visable spectra and molar conductivity. From the above data, the proposed molecular structure for VO(II) complex is squre pyramidal while (Zn(II), Cd(II), Hg(II)) and ( UO2(II),Cr(III)) complexes are forming tetrahedral and octahedral geometry respectively.

Breast mass is by far the most important clinical problem that concerns the breast today. This study was carried out to evaluate diode laser as a cutting tool in breast mass excision and as a hemostatic tool for coagulation during surgery. Using 810 nm diode laser with optical fiber 600μm in diameter of conical tip, udder (cow's breast) tissue, and three female patients (mean age of 35.5 y with clinically palpable breast mass) had been used in this study. The patients were followed up regularly postoperatively. In preliminary work on udder tissue, the power needed for cutting and excision was 15W (power density= 5.3 kW/cm2). The time consumed for excision of a piece of udder tissue, 40×10×3 mm in dimensions was 5 min. The depth range