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 significance of this result is that it is unconditional which means it is proved without assuming any form of strong conjecture like the Elliott–Halberstam conjecture
Summary of the jurisprudence research
Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of the Messengers, our master Muhammad, and upon his pure family, and his ignorant and ignorant companions, and those who followed them in goodness until the Day of Judgment.
Then:
The many jurisprudential aspects that the Shafi’i imams said are of great importance, because these aspects are nothing but the opinions of venerable jurists who have reached a high degree of knowledge until they have become among the owners of faces. And among them are the Shafi’i jurists, the jurists may differ among themselves, either because there is no text about their imam in a
... Show MoreThe research aims at shedding light on the impact of information technology in reducing tax evasion in the General Authority for Taxation. In order to achieve this, the research relied on the analysis of its variables as a main tool for collecting data and information. The results showed that there is a positive and positive effect of information technology on tax evasion. The impact of information technology on increasing tax revenues and reducing the phenomenon of tax evasion In the performance of the research sample, the research sought to highlight the importance of tax information technology through its data and information to the tax administration for the purpose of completing the process Taxpayers for persons subject to income ta
... Show MoreThe present work involved synthesis of several new N-Sulfamethoxazol derivatives imide on Polymeric chain by two steps. The first stip involved preparation of N- (sub.orunsub benzoyl and sub unsub acetyl) amidyl sub sulfamethoxazole (1-5) by condensation of sulfamethoxazole drug with many substituted acid chloride, then the second step include, preparation new five N-(acrly-N–sub or unsub benzoyl) imidyl substituted sulfamethoxazol(6-10) by reaction of poly acryloyl chloride with the prepared compound (1-5) in first stepin asuitable solvent in the presenceamount triethylamine (Et3N) with heating. The structure confirmations of all polymers wereconfirmed using FT-IR,1H-NMR,13C-NMR and UV spectroscopy. Other physical properties including so
... Show MoreThis study examined the effects of water scarcity on rural household economy in El Fashir Rural Council / North Darfur State- western Sudan. Both quantitative and qualitative methods were used as to get a deeper understanding of the impact of water scarcity on the rural house economy in the study area. 174 households out of 2017 were selected from 45 villages which were distributed in eight village councils forming the study area. Statistical methods were used to manipulate the data of the study. The obtained results revealed that water scarcity negatively affected the rural household economy in the study area in many features. These include the followings: much family efforts and time were directed to fetch for water consequentl
... Show MoreHistological study of the cerebellum in a bird white cheeked bulbul Pycnonotus lecucotis, the result of the study showed that the cerebellum took the parts of the hindbrain, the histological study of the cerebellum revealed the presence of deep folds on its surface. The cerebellum consists of two areas, the cerebellar cortex, which is called the gray matter, which consists of three layers: the outer layer (the molecular layer), the middle (Purkinje cells) and inner layer (the granular layer). The second area of the cerebellum is called the medullary and the white matter.
Background: Preparation of platelet-rich fibrin (PRF) is a simple, low cost and minimally invasive method to obtain a natural concentration of autologous growth factors that is widely used to accelerate soft and hard tissue healing, thus, PRF is used in different fields of medicine. The aim of this study was to evaluate the effect of local application PRF on stability of dental implants. Materials and methods: nineteen healthy patients with adequate alveolar bone with two or more adjacent missing teeth and/or bilaterally symmetric to the midline (split-mouth design) missing teeth participated in this study. Each patient received at least two dental implants (Dentium Co., Korea). After surgical preparation of the implant sockets, the PRF was
... Show MoreLeishmania is auxotroph to folic acid,antifolates drug inhibit the synthesis and conversion of folate derivatives. In this study, cytotoxic effect of methotrexate was investigated on the procyclic promastigotes proliferation of L. donovani. The results showed a significant (p ≥ 0.05) difference in growth of treated groups at high concentrations (1000, 500, 250, 125.5) μM after 24, 48 hrs., while at 72 hrs. significant difference was observed at all concentration. The IC50 values was measurable after 24, 48 and 72 hrs. and it was 174.238, 52.283 and 109.175 μM, respectively. The present study showed the cytotoxic effect of methotrexate on the proliferation of promastigotes of the visceral type of Leishmania.
This paper investigates the issue of surface-type effects on traffic noise in Baghdad. Since the raw materials for both flexible and rigid paving are available from local sources, the decision on selecting the type of paving which depends on the budget of the project and the road's importance and function. Knowing that for high traffic volumes and a high percentage of heavy vehicles, rigid pavement is more suitable compared to flexible pavement. In Baghdad, some highways consist of flexible pavement and others of combined pavement (flexible segments and rigid segments), so the study of the effect of surface type on traffic noise becomes an important matter. This study selected three highways: one with flexible pavement a
... Show MoreThe study was enriched by examining (Islamic Sharia’s position on the phenomenon of bullying) becausee bullying is a recurring aggressive behavior that Is one of the types of violence directed by a person or group of prsons; With the intent of deliberately harming and offending anotherr person or group of persons, It has several verbal, physical, electronIc or other formsforms Bullies may follow a policy of Ientimidation or intimidation, as well as ridicule; In order to belittle the victim .The study aims to know the Islamic Sharia ruling on bullying as a modern term for a content that Is as old as man, and the study reached several results, Including: Islam’s affirmation of the prohibition of this phenomenon In word, deed and gesture,
... Show MoreWidely present in the environment, arsenic trioxide has been identified as a genotoxic substance that poses a serious risk to public health. The genotoxic potential of arsenic at low allowable dosage levels is assessed in this study. Four groups of twelve adult rats each were created from the 48 total. Animals in Group I were used as controls Chromosome abnormalities found in bone marrow cells were used to assess the mutagenic potential of arsenic. Hematological parameters were also assessed. At 60 and 90 days, the percentage of microsomal degranulation in the hepatic fraction increased and the amounts of RNA and proteins considerably reduced (P < 0.01) in all three dosages given. was employed in order to assess hematological par
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