Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

Reflective cracking is one of the primary forms of deterioration in pavements. It is widespread when Asphalt concrete (AC) overlays are built over a rigid pavement with discontinuities on its surface. Thus, this research work aims to reduce reflection cracks in asphalt concrete overlay on the rigid pavement. Asphalt Concrete (AC) slab specimens were prepared in three thicknesses (4, 5, and 6 cm). All these specimens were by testing machine designed and manufactured at the Engineering Consulting Office of the University of Baghdad to examine for the number of cycles and loads needed to propagate the reflection cracking in the asphalt concert mixture at three temperatures (20, 30, and 30°C). It was noticed that the higher thickness A

Abstract

 Experimental work from Magnetic Abrasive Finishing (MAF) tests was carried out design parameters (amplitude, and number of cycle which are formed the shape of electromagnetic pole), and technological parameters (current, cutting speed, working gap, and finishing time) all have an influence on the mechanical properties of the surface layer in MAF process. This research has made to study the effect of design and technological parameters on the surface roughness (Ra), micro hardness (Hv) and material removal (MR) in working zone. A set of experimental tests has been planned using response surface methodology according to Taguchi matrix (3⁶) with three levels and six factors

In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is

Background: Smoking is the major environmental risk factor that has been associated with the pathogenesis and progression of periodontal diseases. Interleukin-8 (IL-8), has been associated with the immunopathology of periodontitis. Objectives: To determine the influence of smoking on salivary Interleukin-8 level from smokers and non-smokers with periodontitis and periodontally healthy control subjects.

Materials and Methods: Un-stimulated saliva samples were collected of 90 participants: 30 smokers and 30 non-smokers with chronic periodontitis, as well as 30 periodontally healthy control subjects. The clinical parameters such as the pocket depth, clinical attachment loss, plaque index, and gingiv

The Impact of Intellectual trends on the nature of the Economic Structure of Iraq

Experimental investigations had been done in this research to demonstrate the effect of carbon fiber and Ceramic fillers contents on the tribological behaviour of (15% volume fraction) carbon-epoxy composite system under varying volume fraction, load, time and sliding distance. The wear resistance were investigated according to ASTM G99-05standard using pin on disc machine to present the composite tribological behaviour. The influence of three ceramic fillers, granite, perlite and calcium carbonate (CaCO₃), on the wear of the carbon fabric reinforced epoxy composites under dry sliding conditions has been investigated. The effect of variants in volume fraction, applied load, time and sliding distance on the wear behaviour of po