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.

This study was designed to highlight the role of Epstein Barr viruses (EBV) as a possible causative effect in multiple sclerosis (MS) through testing the viral load along with both biochemical and immunological parameters in female MS patients. We also aimed at finding the effects of different types of treatment line on the various study aspects. The results of the enzyme-linked immunosorbent assay (ELISA) revealed first an increased level of EBV EBNA1IgG IL-17A (96.13±27.60 pg/ml) in sera of female MS patients (0.05±0.01 U/ml, n=50) compared with the control group (n=40). We confirmed this result using real-time polymerase chain reaction (RT-PCR) which also showed a significantly higher EBV load in MS patients (22.61±12.72 copi

This research aims to identify the role of external environment factors on the quality of educational services, from the academic point of view, where the distribution of a questionnaire to a random sample of (100) university professors, and then analyzing a model, and test the validity of this model using structural modeling (SEM) (Structural Equation Modeling).
And then test the relationships between variables using the software of Statistical Package for Social Sciences (SPSS V.18), the research found a number of conclusions, the most important conclusion is: the external environment factors has significant impact on the quality of educational services.

It was found that there was a significant correlation between all tests of the mechanical and electrical activity of the heart (systolic force FC, stroke volume SV, end-diastolic volume, EF volume, and left ventricular volume during diastole LVDD) with the test of the oxygen-phosphating energy system (Markaria). - As safe (Margaria-Kalamen( It was found that there is a significant correlation between all tests of the mechanical and electrical activity of the heart (myocardial systolic force FC, stroke volume SV, end-diastolic volume EDV, and the percentage of heart pumpingEF blood, and left ventricular volume during diastole (LVDD) with the Lactational Oxygen Energy System Test (Wingate Test 30 Second(

This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given.  As the first result, it has been proved that every  σ-algebra over a fuzzy set x*  is a  fuzzy σ-ring-over a fuzzy set x*  and construct their converse by example. Furthermore, the fuzzy ring  concept has been studied to generalize fuzzy algebra and its relation. Investigating  that the concept of fuzzy  σ-Ring is a stronger form of a fuzzy ring  that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied

Bipedal robotic mechanisms are unstable due to the unilateral contact passive joint between the sole and the ground. Hierarchical control layers are crucial for creating walking patterns, stabilizing locomotion, and ensuring correct angular trajectories for bipedal joints due to the system’s various degrees of freedom. This work provides a hierarchical control scheme for a bipedal robot that focuses on balance (stabilization) and low-level tracking control while considering flexible joints. The stabilization control method uses the Newton–Euler formulation to establish a mathematical relationship between the zero-moment point (ZMP) and the center of mass (COM), resulting in highly nonlinear and coupled dynamic equations. Adaptiv

The bifurcation of the constitutional rights of one of the techniques used by the constitutional court to expand the scope of the constitutional right to explicit, and access to the fact that guarantees constitutional rights, and establishes the constitutional elimination of this technique on a particular bond is the constitutional terms of reference, and in the light of his discretion in the exercise of the constitutional powers of , and tends at times To the adoption of a broad branching approach, which confers on the constitutional text containing constitutional rights a wider scope than the scope of an explicit right.

Background: we know that TNF-a which is consider an important inflammatory cytokine mediate the inflammatory reactions which occur in the tissues against the infections agents and other causes of inflammation therefore, here we try to study the role of TNF-a in chronic Rheumatic heart disease and the relationship of TNF-a with extent of histopathological.

Transport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,