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.

This study evaluates the flexural behavior of ultra-thin (50 mm) one‑way reinforced‑concrete (RC) slabs retrofitted with near‑surface mounted (NSM) carbon‑fiber‑reinforced polymer (CFRP) rods under quasi‑static loading. T300‑grade CFRP rods (≈4 mm diameter) were bonded in pre‑cut 7 mm × 7 mm grooves using a two‑part epoxy. As a proof-of-concept experimental baseline, three simply‑supported specimens (1000 mm × 500 mm × 50 mm) were tested in a six‑point bending configuration (four applied loads + two reactions): two conventional controls and one strengthened slab. A load‑control rate of ~15 kN/min was applied; the controls were cycled twice and the strengthened slab four times. Relative to the average of

Now-a-days the Flexible AC Transmission Systems (FACTS) technology is very effective in improving the power flow along the transmission lines and makes the power system more flexible and controllable. This paper deals with the most robust type of FACTS devices; it’s a Unified Power Flow Controller (UPFC). Many cases have been taken to study how the system behaves in the presence and absence of the UPFC under normal and contingency conditions. The UPFC is a device that can be used to improve the bus voltage, increasing the loadability of the line and reduce the active and reactive power losses in the transmission lines, through controlling the flow of real and reactive power. Both the magnitude and the phase angle of th

Numerical study has been conducted to investigate the thermal performance enhancement of flat plate solar water collector by integrating the solar collector with metal foam blocks.The flow is assumed to be steady, incompressible and two dimensional in an inclined channel. The channel is provided with eight foam blocks manufactured form copper. The Brinkman-Forchheimer extended Darcy model is utilized to simulate the flow in the porous medium and the Navier-Stokes equation in the fluid region. The energy equation is used with local thermal equilibrium (LTE) assumption to simulate the thermofield inside the porous medium. The current investigation covers a range of solar radiation intensity at 09:00 AM, 12:00 PM, and 04:00

     The General Company for Iraqi Cement is regarded as one of the companies that contribute to support the Iraqi economy. It contributes to provide the material of cement which fulfils the consumer and investment need in the markets in competitive prices and not to resort to the importing of the cement from abroad. That would save a great share of the purchase parity of the poor sectors of society. The estimation  of production function will contribute to putting the company.

The application functions of  the standard production of  benefit critical to clarify the actual relationship between production & its components, & allow to clarify the i

Abstract

 The problem of missing data represents a major obstacle before researchers in the process of data analysis in different fields since , this problem is a recurrent one in all fields of study including social , medical , astronomical and clinical experiments .

The presence of such a problem within the data to be studied may influence negatively on the analysis and it may lead to misleading conclusions , together with the fact that these conclusions that result from a great bias caused by that problem in spite of the efficiency of wavelet methods but they are also affected by the missing of data , in addition to the impact of the problem of miss of accuracy estimation

Nigella sativa seeds (NSS) are reputed traditionally and scientifically as a potent agent that promote milk secretion (galactagogue), but their mechanism of action is studied trivially. One suggestion was that these seeds are bio-transformed to sex hormones within the ovaries. Therefore, this investigation was designated to throw light on the action of these seeds in the absence of ovaries i.e. in male rats. Thirty Norway male albino rats were used in this investigation. They were divided into experimental (n=20,fed NSS 2g/ Kg body weight /day for 14 days) and control (n=10, fed placebo for 14 days). After sacrifice mammary gland and blood samples were obtained. Experimental rats revealed a significant increase (p (0.01>in