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
ABSTRACT : This research involves the synthesis of five to seven heterocyclic compounds starting with Schiff’s bases which derived from oxime as a starting material. 1.3-oxazepine derivatives were prepared from adding different anhydrides to the Schiff bases, tetrazole and thiazolidinone derivatives synthesized from add sodium azide and thioglycolic acid to the same Schiff’s bases as a five members ring. Pyrimidine derivatives were prepared after the reaction of the azomethine group with acetyl chloride and then urea and thiourea to synthesis on derivatives contain the six members ring. Another step included identified and confirmed these compounds by FT- IR, 1HNMR, TLC and 13CNMR finally, step included the assay of biological activity
... Show MoreBackground : Although development and progress in various diagnostic methods, but still identification of remnants of skeletal and decomposing parts of human is one of the most difficult skills in forensic medicine . Gender and age estimation is also considering an important problem in the identification of unknown skull. The aims of study: To estimate volume and dimension of maxillary sinus in individuals with dentate and edentulous maxillae using CT scan, and to correlate the maxillary sinus volume in relation to gender and age. Materials and Methods : This study included 120 patients ranged from (40-69 years), divided into two groups, dentate group with fully dentate maxilla and edentulous group with complete edentulous maxilla, and e
... Show MoreInflammatory response had a role in cancer progression, presence of noticeable inflammation within the tumor and its margin may play an important prognostic role in colorectal carcinoma.
Background: Oral SCC is a complex malignancy where environmental factors, viral infections and genetic alterations most likely interact, and thus give rise to the malignant condition. The HSP70 play a direct role in apoptosis inhibition by aligning the improved integrity of a cell’s proteins with the improved chances of that particular cell’s survival.P21 gene produces p21 protein which is a potent cyclin-dependent kinase inhibitor that plays a significant role in carcinogenesis. The aims of the study were to evaluate and compare the immun-histochemical expression of the HSP70 and cell cycle protein p21in NOM, OED, and OSCC. Correlate both marker expressions with each other. Materials and methods: Forty six formalin-fixed, par
... Show MoreThe present study aimed to use the magnetic field and nanotechnology in the field of water purification, which slots offering high efficiency to the possibility of removing biological contaminants such as viruses and bacteria rather than the use of chemical and physical transactions such as chlorine and bromine, and ultraviolet light and boiling and sedimentation and distillation, ozone and others that have a direct negative impact on human safety and the environment. Where they were investigating the presence in water samples under study Coli phages using Single agar layer method and then treated samples positive for phages to three types of magnetic field fixed as follows (North Pole - South Pole - Bipolar) and compare the re
... Show MoreA new Schiff base ligand [L] [3-methyl-9,10 phenyl -6,7 dihydro-5,8 –dioxo-1,2 diazo –cyclo dodecu 2,11-diene ,4-one ] and its complexes with (Co(II), Ni(II), Cu (II), Zn(II) and Cd(II)) were synthesis.This ligand was prepared in three steps, in the first step a solution of salicyladehyed in methanol reacted under refluxed with hydrazine monohydrate to give an (intermediate compound 1) which reacted in the second step with sodium pyruvate to give an (intermediate compound 2) which gave the ligand [L] in the three step when it reacted with 1,2- dichloro ethane.The complexes were synthesized by direct reaction of the corresponding metal chloride with the ligand. The ligand and complexes were characterized by spectroscopic methods [IR, UV-
... Show MoreBackground: This study aimed to determine whether there is a relationship among the bite force with facial dimensions and dental arches in a sample of Iraqi adults with Class I skeletal and dental relations. Materials and methods: Forty dental students (20 males and 20 females) were selected under certain criteria. For those individuals, dental impressions, frontal facial photographs and maximum bite force at molar and incisor regions were taken. The dental arches widths and facial dimensions were measured using the AutoCAD program 2007, while the bite force was determined using special device. Descriptive statistics for the measured variables were performed and gender difference was determined using independent sample t-test, while the rel
... Show MoreA new mixed ligand complexes were prepared by reaction of quinoline -2-carboxylic acid (L1) and 4,4?dimethyl-2,2?-bipyridyl (L2) with V(IV),Cr(III), Rh(III), Cd(II) and Pt(IV) ions. These complexes were isolated and characterized by (FT-IR) and (UV-Vis) spectroscopy, elemental analysis, flame atomic absorption technique, thermogravimetric analysis, in addition to magnetic susceptibility and conductivity measurements. Most complexes were mononuclear and with octahedral geometry, except Cd (II) with tetrahedral geometry, and V (IV) with square pyramidal geometry. A theoretical treatment of the ligands and the prepared complexes in gas phase was done using two programs Hyperchem.8 and Gaussian program (GaussView Currently Available Versions (
... Show MoreThe present work includes the preparation and characterization of{Co(II) , Ni(II), Pd(II), Fe(III) , Ru(III),Rh(III), Os(III) , Ir(III) , Pt(IV) and VO(IV)}complexes of a new ligand 4-[(1-phenyl-2,3-dimethyl-3-pyrozoline-5-one)azo]-N,N-dimethylanline (PAD). The product (PAD) was isolated,studies and characterized by phsical measurements,i.e., (FT-IR), (UV) Spectroscopy and elemental analysis(C.H.N). The prepared complexes were identified and their structural geometric were suggested in solid state by using flame atomic absorption, elemental analysis(C.H.N), (FT-IR) and (UV-Vis) Spectroscopy, as well as magnetic susceptibility and conductivity measurements . The study of the nature of the complexes formed in( ethanolic solution) following t
... Show MoreThe reaction of [Benzoyl hydrazine] with [Diphenyl mono oxime] and Glacial acetic acid was carried out in methanol gave a new tridentate ligand [Benzoic acid (2- hydroxyimino- 1, 2-diphyneylethylidene) - hydrazide]. This ligand was reacted with some metal ions (Fe(II), Co(II), Ni(II), and Cu(II)) in methanol with (1:1) metal : ligand ratio to give a series of new complexes of the general formula [M(L)Cl2.H2O], where M= Fe(11), Co(11), Ni(11) and Cu(11) . All compounds were characterized by spectroscopic methods (I.R, UV-Vis), elemental microanalysis (C.H.N), atomic absorption, magnetic susceptibility, and conductivity measurements. From the obtained data the proposed molecular structures were suggested for the complexes of Fe (II), Co (II)
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