Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

إن دراسة طبيعة الحياة السياسية والحزبية والبرلمانية ومميزات الشعب السويدي الهدف منها من اجل فهم أفضل لبلد هو السويد يقع في أقصى شمال اوربا والعالم يسعى العراق الى تطوير علاقاته معه على كافة الصعد السياسية والاقتصادية والاجتماعية والثقافية والعلمية والتجارية والعسكرية، وفي نفس الوقت الذي تسعى السويد من جانبها لتوثيق هذه العلاقات من واقع معرفتها بمكانة العراق الحضارية والنفطية والاستثمارية والاقتصادية و

أن استقراء تاريخ العلاقات الامريكية- العراقية وما أفرزته تفاعلاتها من احداث وسلوكيات، نجد ان الولايات المتحدة الامريكية منذ نشوئها كدولة مستقلة وفي ضوء اعتبارات النشأة والتكوين لأنها قامت على اساس مبدأ جوهري الا وهو مبدأ البراغماتية واغتنام الفرص والتوسع على حساب الاخر، وعليه فان العراق قد استحوذ على مكانة محورية في المدرك الاستراتيجي الامريكي، لاسيما قبل الحرب العراقية- الايرانية، فضلا عن ان موضوع البح

In this research, titanium dioxide nanoparticles (TiO₂ NPs) were prepared through the sol-gel process at an acidic medium (pH3).TiO₂ nanoparticles were prepared from titanium trichloride (TiCl₃) as a precursor with Ammonium hydroxide (NH₄OH) with 1:3 ratio at 50 °C. The resulting gel was dried at 70 °C to obtain the Nanocrystalline powder. The powder from the drying process was treated thermally at temperatures 500 °C and 700 °C. The crystalline structure, surface morphology, and particle size were studied by using X-ray diffraction (XRD), Atomic Force Microscopy (AFM), and Scanning Electron Microscope (SEM). The results showed (anatase) phase of titanium dioxide with the average grain size

This paper deals with defining Burr-XII, and how to obtain its p.d.f., and CDF, since this distribution is one of failure distribution which is compound distribution from two failure models which are Gamma model and weibull model. Some equipment may have many important parts and the probability distributions representing which may be of different types, so found that Burr by its different compound formulas is the best model to be studied, and estimated its parameter to compute the mean time to failure rate. Here Burr-XII rather than other models is consider  because it is used to model a wide variety of phenomena including crop prices, household income, option market price distributions, risk and travel time. It has two shape-parame

Background: intravenous regional anaesthesia (IVRA) is an effective method of producing anaesthesia of the extremities. Disadvantages are the rapid loss of anaesthesia after the deflation of the tourniquet and the rapid development of postoperative pain. It is important to search for agents with longer durations of action, better nerve fibre selectivity, lesser degrees of motor blockade and lower incidences of systemic toxicity.Objectives: This study was designed to evaluate and compare the clinical effects of intravenous regional anaesthesia, with lidocaine alone, or in a combination with ketamine and atracurium for better analgesia, and to examine the possible clinical advantages of using muscle relaxants (i.e., atracurium) with intrav

The Central Marshes are one of southern Iraq's most important wetlands and ecosystems. A study on evaluating soil quality and water quality in terms of chemical properties at certain sites in the southern Iraqi Central Marshes has been conducted to investigate their types and suitability for enhancing the agricultural reality of most field crops. Soil and water samples were collected from 15 sites and transferred to the laboratory. In the lab, the following parameters were determined: electrical conductivity (EC), total dissolved salts (TDS), organic materials (OM), pH, gypsum, and total sulfate content (SO₃). The tests conducted on the samples indicated that it could be said that the soil of the Central Marshes

Fusarium pseudograminearum and Fusarium graminearum commonly cause crown rot (FCR) and head blight (FHB) in wheat, respectively. Disease infection and spread can be reduced by the deployment of resistant cultivars or through management practices that limit inoculum load. Plants deficient in micronutrients, including zinc, tend to be more susceptible to many diseases. On the other hands, and zinc deficiency in cereals is widespread in Australian soils. Zinc deficiency may have particular relevance to crown rot, the most important and damaging Fusarium disease of wheat and barley in Australia. Four wheat genotypes; Batavia, Sunco and two lines from the International Maize and Wheat Improvement Center (CIMMYT) were tested for response