The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
Background: Using dual-energy X-ray absorptiometry, body fat mass has been determined. The assessment of body fat mass was conducted utilizing dual-energy X-ray absorptiometry analysis of the pelvis and vertebral column. While it is acknowledged that osteoporosis can impact both body fat mass and bone mineral density, the particulars of this relationship currently remain uncertain. Objective: The aim of the present investigation is to assess gender differences in the effects of osteoporosis on the body fat mass of the upper and lower extremities. Method: 170 individuals participated (85 males and 85 females) in this study. Patients who presented with bone discomfort consisted of 40 males and 40 females. In addition, 90 apparently he
... Show MoreLaser drilling is capable of producing small, precisely positioned holes with high degree of reproductively. In this paper , IR millisecond Nd:YAG single pulsed laser was used to determine the effect of laser parameters on the drilled hole of the glass - fiber reinforced epoxy composite FR-4 sample of 2 mm in thickness . The type of laser source was GSI lumonics JK760TR Series laser 1.064μm system in a CNC cabin. The JK760TR series has a 0.3-50ms pulse length and a maximum repetition rate 500Hz with an average power of 600W. The investigation of single pulse laser drilling in this paper was based on theoretical and experimental solutions. In single pulse technique, the investigation included focal plane position fpp, pulse shap
... Show MoreIn this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.
The child realize that the meals time provide golden opportunities to get the attention the child needs. However, many difficulties that may appear about eating food can be avoided, if the family used the right way in dealing with this problem. The study aims, in this case, at searching for the reasons that lies behind the child's obstinacy in eating his food and the attempt to study some variables that is related to the research topic.
The results are summed up as follows:
- The number of the sample children is 3 of both sexes between the ages of 3 to 6 years
The ï€ ï¤
Mixing ratios of ï€ ï§
transitions from low and high spin states populated from the nuclear reaction Ni Mg pn Y 80 39 58 28 ( , ) ï§ are calculated using a new method which we called it as Improved Analysis Method. The comparison of the results of experimental values,CST method, LST and adopted ï€ ï¤ mixing ratios with the results of the presented work confirm the validity of this method.