The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
Background: The clinical examination is one of the best suitable methods for diagnosis of low backache. Backache is one disease that the signs, clinical examination finding, and the results on imaging modalities not always related. The straight leg raising (SLR) and slump tests, can be used for diagnosis of lumber disc herniation.
Objectives: To compare the result of the slump test and SLR test in the diagnosis of lumber disc herniation.
Subjects and Methods: A prospective comparative study conducts on 280 patients in Al-Kindy teaching and private clinics complaints of backache, aging between 18-70 years old with acute or recurrent backache, sciatica pai
... Show MorePoisoning with toxic substances accidently or deliberately can be life threatening and especially in some countries that lack the essential tests and facilities to identify the types and causes of these toxic substances. In Iraq, as many other countries, poisoning is one of the chronic public health problems. However, very little literature about the pattern of poisoning cases, types and age is available in Duhok Governorate. Therefore, this study was conducted to determine the most common patterns of poisoning and the related age and gender in Duhok Governorate from 2016-2018, which would possibly contribute to the early diagnosis and treatment of poisoning. The present study was conducted for three years, started from 1st of
... Show More The TV has the ability to combine sound and picture, which makes it of a direct impact on the recipient as it is a rich communicative tool with various artistic forms that display through this small screen programs and films, so that the TV has become superior over many other means of communication.
This research is concerned with the technical and artistic ability in the production of programs owned by the TV as a means of attraction of educated children aged between 5-12 years old, which makes it an educational supplement for the school that helps them in providing knowledge, acquiring skills and being informed about the different sciences through educational programs. It is known that the child at this stage enjoys when wa
In light of increasing demand for energy consumption due to life complexity and its requirements, which reflected on architecture in type and size, Environmental challenges have emerged in the need to reduce emissions and power consumption within the construction sector. Which urged designers to improve the environmental performance of buildings by adopting new design approaches, Invest digital technology to facilitate design decision-making, in short time, effort and cost. Which doesn’t stop at the limits of acceptable efficiency, but extends to the level of (the highest performance), which doesn’t provide by traditional approaches that adopted by researchers and local institutions in their studies and architectural practices, limit
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This study aims to identify the issue of observing media publishing and its importance for public relations in the management of special events; and its role in building the positive image of the target audience through communication messages that illustrate the political, economic and diplomatic importance of the Arab Summit. As such Summit is one of the conferences that Iraq sought to secure the requirements of its convening to re-activate its political and diplomatic role in the Arab Ocean, especially after the circumstances and crises that Iraq went through.
The convening of the Arab Summit under the auspices of Iraq was a qualitative transition, during which Iraq sought to achieve some gains b
... Show MoreAfter the persistence of the British policy of oppression and control over the American colonies and the attempts to obliterate the identity of their inhabitants, the colonies worked on moving forward towards achieving independence, and Virginia was the first to initiate the development of the new government frameworks, through George Mason in drafting the Virginia Bill of Rights in 1776, which expressed the philosophy of the era Enlightenment and independent revolutionary thought, which called for equality and natural rights for individuals and the need for a free popular government that works for the common good.
Background: The incorporation of rubber has not been entirely successful because it can have detrimental effects on the transverse Strength and hence the rigidity of the denture base. Materials and methods: Zirconium oxide nanoparticales were coated with a layer of trimethoxysilylpropylmethacrylate (TMSPM) before sonication in monomer (MMA) with the percentages 3% by weight then mixed with powder using conventional procedure.(100) samples were prepared and divided into five groups according to the test performed ,Each group consisted of 20 specimens and these were subdivided into 2 groupsGroup (A): control group (10 specimens of high impact acrylic resin without zirconium oxide) and Group (B):zirconium oxide group(10 specimens of high impac
... Show MoreNonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic
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