Let A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with  is the same for all . Here  is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i

In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials

In this paper a Г-ring M is presented. We will study the concept of orthogonal generalized symmetric higher bi-derivations on Г-ring. We prove that if M is a 2-torsion free semiprime    Г-ring ,  and  are orthogonal generalized symmetric higher bi-derivations  associated with symmetric higher bi-derivations   respectively for all n ϵN.

In this paper, we generalized the principle of Banach contractive to the relative formula and then used this formula to prove that the set valued mapping has a fixed point in a complete partial metric space. We also showed that the set-valued mapping can have a fixed point in a complete partial metric space without satisfying the contraction condition. Additionally, we justified an example for our proof.

Application of pesticide on vegetables will protect them from pest injury, but in another hand will hold pesticide residues inside vegetables. These residues have harmful effect against all consumers. Detection about pesticide residues has been carried out for some Iraqi vegetables (tomato, cucumber, eggplant, and zucchini) by using Gas Chromatography/Mass Spectroscopy (GC/MS). (Quick, Easy, Cheap, Effective, Rugged, and Safe) QuEChERS method has been applied for extraction pesticide residues from targeted vegetables. The GC/MS has been carried out before the treatment of residues for distinguish the vegetables that are suffering from hyper concentration in pesticide residues more than maximum residues limits (MRLs). Three kinds of solut

  The ceramics specimens as superconducting phase (Bi2PbxSr2Ca2Cu3O10+δ) with different concentrations of Pb from (0.0-0.5) were prepared by solid-state reaction method. Superconducting samples were exposed to high humidity (RH 75% at 25ºC) for seven weeks time interval. The humidity has a negative effect on the transition temperature of superconductor phase .It destroys the superconducting phase and the samples were converting to insulator.  
 

The purpose of this research is to introduce a concept of general partial metric spaces as a generalization of partial metric space. Give some results and properties and find relations between general partial metric space, partial metric spaces and D-metric spaces.

            This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.