In this paper the chain length of a space of fuzzy orderings is defined, and various properties of this invariant are proved. The structure theorem for spaces of finite chain length is proved. Spaces of Fuzzy Orderings Throughout X = (X,A) denoted a space of fuzzy orderings. That is, A is a fuzzy subgroup of abelian group G of exponent 2. (see [1] (i.e. x 2 = 1,  x  G), and X is a (non empty) fuzzy subset of the character group  (A) = Hom(A,{1,–1}) satisfying: 1. X is a fuzzy closed subset of  (A). 2.  an element e  A such that (e) = – 1    X. 3. X :={a  A\ (a) = 1    X} = 1. 4. If f and g are forms over A and if x  D(

     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.

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.

The research dealt with the study (interpretation of space in the art of installation), and it is located in four frameworks, the first is devoted to clarifying the research problem, its importance and the need for it, its goal, and its limits, and determining the most important terms contained therein.The research problem was determined from the question, does space embody those different and diverse materials that were formulated and installed by the artist into modern forms? Is the product of synthetic arts an appropriation of these spaces and domination of them?The problematic of interpreting space in its conceptual dimension in (synthetic) art in its multiplicity, diversity and difference, or objecting to the work of artistic system

Background: Thalassemia is a form of inherited autosomal recessive blood disorder characterized by abnormal formation of hemoglobin.
Objective: Determine frequencies & association of HLA class II alleles (DRB1& DQB1) in Iraqi β-thalassemia major patients.
Patients: seventy unrelated randomly selected β-thalassemia major patients, and one hundred unrelated randomly selected healthy individuals, composed the control group.
Methods: low resolution PCR-SSO (Sequence Specific Oligonucleotide) technique was used for HLA typing.
Results: HLA DQB1*5 give significance importance as an etiological risk factor for β-thalassemia major; HLA DQB1*3 give significance importance as a preventive risk factor for β-thalassemia major

In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of D-operators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator.

BACKGROUND: Femoral shaft fracture is a common fracture in pediatric age group reaching 62% of all fracture shaft femur in children in spite of rapid union rate and successful conservative treatment but some cases need surgical intervention and one of the methods using plate and screw by the lateral approach. AIM: This study aims to compare functional outcome fixation of mid-shaft femur fracture in children by plate and screws between (subvastus lateralis and transvastus lateralis) regarding infection, union, and limitation of knee movement. PATIENT AND METHOD: The study was done on 30 children who had diaphyseal fracture femur in Al-Kindy Teaching Hospital in period (April 2018–April 2020) with 6 months follow-up, and the pa

Background: TIDM is known to be polygenic disease that appears from the interaction of mutation in multiple genes including HLA. The autoimmune mediated destruction of
pancreatic β-cells is reflected by the presence of autoantibodies against prominent antigens in the pancreatic β-cells.
Objective: This study was designed to investigate the role of HLA-class I and class II antigens in the etiology of type 1 diabetes mellitus (T1DM) and also assessment of
glutamic acid decarboxylase (GAD65) autoantibodies in the patients at the onset of the disease.
Patients & Methods: Sixty T1DM patients who were newly onset of the disease (diagnosed less than five months) were selected. Eighty apparently healthy

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.