In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

          The present paper studies the generalized Φ-  recurrent of Kenmotsu type manifolds. This is done to determine the components of the covariant derivative of the Riemannian curvature tensor. Moreover, the conditions which make Kenmotsu type manifolds to be locally symmetric or generalized Φ- recurrent have been established. It is also concluded that the locally symmetric of Kenmotsu type manifolds are generalized recurrent under suitable condition and vice versa. Furthermore, the study establishes the relationship between the Einstein manifolds and locally symmetric of Kenmotsu type manifolds.

In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule  of an -module  is called an approximaitly prime submodule of  (for short app-prime submodule), if when ever , where , , implies that either  or . So, an ideal  of a ring  is called app-prime ideal of  if   is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.

        The purpose of this work is to construct complete (k,n)-arcs in the projective 2-space PG(2,q) over Galois field GF(11) by adding some points of index zero to complete (k,n–1)arcs 3 ï‚£ n ï‚£ 11.         A (k,n)-arcs is a set of k points no n + 1 of which are collinear.         A (k,n)-arcs is complete if it is not contained in a (k + 1,n)-arc

n this research, some thermophysical properties of ethylene glycol with water (H2O) and two solvent mixtures dimethylformamide/ water (DMF + H2O) were studied. The densities (ρ) and viscosities (η) of ethylene glycol in water and a mixed solvent dimethylformamide (DMF + H2O) were determined at 298.15 K, t and a range of concentrations from 0.1 to1.0 molar. The ρ and η values were subsequently used to calculate the thermodynamics of mixing including the apparent molar volume (ϕv), partial molar volume (ϕvo) at infinite dilution. The solute-solute interaction is presented by Sv results from the equation ∅_v=ϕ_v^o+S_v √m. The values of viscosity (B) coefficients and Falkenhagen coefficient(A) of the Jone-Dole equation and Gibbs free

          Measurements of excess molar volumes V^E , viscosities η , excess viscosities Δ ln η  and excess molar activation energies of viscous flow ΔG^E , are reported for binary mixtures of dimethylformamide (DMF) with , benzene , o-xylene , 1,4- dioxane and tetrahydrofuran are reported from density and viscosity measurements at 298.15 k and at atmospheric pressure over the entire composition range . The excess values are positive for the mixture (DMF+ polar solvent) and negative deviation from ideality for the mixture (DMF + non-polar solvent) over the whole composition range and discussed in the light of molecular interaction in the mixture.

The present study was carried to evaluate antibacterial activity of Acetone, Alcholic (cold and hot) and Aqueaus(water) extracts of Citrus aurantifoliaseeds,against growth of some bacteria isolated from burns infections(Pseudomonas aeruginosa,Escherichia coli, Klebsiellapneumonia,Staphylococcusaureus)fromKindy HospitalIn Baghdad from March to June 2012.Antibiotic Sensitivity was done for all isolated bacteria used in this study.Results showed variation in antibacterial activity of different extracts against all tested bacteria by well diffusion technique in agar and measuring the diameter of inhibition zone, at concentration 250Mg-ml. Acetone extract had the greatest inhibitory effect followed by hot alcoholci extract, and then cold alcohol

The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R. Then T is a left (right) ?-centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where ? be surjective endomorphism of R . It is also proved that if T(x?y)=T(x)??(y)=?(x)?T(y) for all x, y ? R and ?-centralizers of R coincide under same condition and ?(Z(R)) = Z(R) .

Background: Oral anticoagulation medication, warfarin and non-vitamin k antagonist oral anticoagulants  (NOAC) may require long term use which may affect patients’ satisfaction with their treatment and their quality of life (QOL). Objective: To compare the quality of life and treatment satisfaction among groups of patients using different anticoagulant therapies (warfarin and NOAC). Patients and methods: A cross-sectional study was performed at Ibn Al-Bitar Hospital for cardiac surgery in Baghdad in the period between December 2022 to May 2023. The study population included a convenient sample of patients receiving either warfarin or non-vitamin k antagonist oral anticoagulants treatment. The Arabic version of the short form 12