This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

A great abbey in the Shari'a, and is therefore destined to be preserved in many texts and by methods
There are many prayers in the Qur'an and Sunnah to encourage them
They have a clear relationship with the preservation of the purposes of the Sharia in general, and with a purpose
Save the mind in particular, but the scholars - the mercy of God - when they declare that the costs of Sharia
Due to the preservation of my intentions in the creature, they limit their words to orders and intentions, and are not exposed
In particular,
If they were included in the texts of the Shariah and Tawjiyatiya,
To be related to the preservation of the purposes of the law, which confirms the words of the former leaders, and light the li

Praise be to God alone, and after:

This is a research entitled: “A fundamental study of judicial jurisprudence rules and their applications in the Hanbali school of thought,” in which the researcher studied eight legal jurisprudential rules considered by the Hanbalis and others.

At the conclusion of his research, the researcher reached a number of results, including: the importance of taking care of judicial rules, and the need for judges and their assistants to them, including: the need for students of science in Hanbali jurisprudence to study these rules according to the doctrine, and to highlight their applications to them, including: the importance of the rules under study, and their impact on rulings Jurisprudenc

     2-amino-5-mercapto-1,3,4-thiadiazole [I] were prepared by the cyclization of thiosemecarbazide with carbon disulphide and anhydrous  sodium carbonate in ethanol as a solvent. The reaction of compound [I] with alkyl halides yielded 2- amino-5-thioalkyl-1,3,4- thiadiazole [II] and [III] . Compound [II] and [III] were reacted with different aromatic aldehydes to yieled 2-[(substituted benzyliden ) amino] -5- thioalkyl-1,3,4- thiadiazole [IV]a-c , [V]a-d and [VI]a-d .  Schiff ,s bases [IV]a-c , [V]a-d and [VI]a-d  were found to react with  2mercapto benzoic acid in the triethyl amine to give 3-[ 5-( alkylthio) -1,3,4- thiadiazol-2-yl] 2,3- dihydro- 2- (aryl) benzo [e] [1,3] thiazine -4-one [VII]a-

     Creatinine and Schiff`s bases are well known for their diverse range of biological activities and are thought to be emerging and useful therapeutic targets for the treatment of several diseases. The present work was aimed at the synthesis of new imidazolidine-4-one, thiazolidine-4-one, and oxazolidine-4-one derivatives derived from creatinine and to illustrate their influence on a colon cancer cell line and assess their antioxidant activity. Creatinine was reacted with α-chloroethyl acetate to produce 2-ethyl acetate creatinine 1. Then, the reaction of compound  1 with n-propyl bromide afforded N-propyl-2-ethylacetate creatinine 2. Compound 2

The reaction of 2, 4, 6-trihydroxyactophenonemonohydrate with hydrazine monohydrate was realized under reflux in methanol and a few drops of glacial acetic acid were added to give the (intermediate) 2-(1-hydrazono-ethyl)-benzene-1, 3, 5-triol, which reacted with salicylaldehyde in methanol to give a new type (NO) ligand [HL][(2-1-[(2-hydroxy-benzyliidene)-hydrazono]-ethyl) benzene-1, 3, 5-triol. The ligand was reacted with Mcl.(where M-Co, Ni, Cu, and Zn) under reflux in methanol with (l: 1) ratio to give complexes of the general formula [M (HL)]. All compounds have been characterized by spectroscopic methods I" H NMR, IR. UV-Vis, HPLC, atomic absorption] microanalysis along with conductivity measurement. From the above data the proposed mo

This comprehensive review examines the efficacy and safety of tumor necrosis factor-alpha (TNF-α) inhibitors in treating various autoimmune diseases, and focuses on their application in Iraqi patients. Elevated TNF-α levels are linked to autoimmune disorders, leading to the development of anti-TNF-α therapies such as infliximab, etanercept, adalimumab, certolizumab pegol, and golimumab, which have gained FDA approval for conditions like psoriasis, in¬flammatory bowel disease, ankylosing spondylitis, and rheumatoid arthritis. While these therapies demonstrate sig¬nificant therapeutic benefits, including improved quality of life and disease management, they also carry risks, such as increased susceptibility to infections and pote

Ankylosing spondylitis (AS) is a common, highly heritable inflammatory arthritis affecting primarily the spine and pelvis. This study was aimed to investigate the relationship between the rs27044 polymorphism in Endoplasmic reticulum aminopeptidase-1 (ERAP-1) with the susceptibility and severity of AS correlated with some biochemical markers such as hematological parameter (Erythrocytes sedimentation rate (ESR)) and immunological parameters (C-reactive protein (CRP), Human leukocyte antigen-B27 (HLA-B27), Interlukin-6 (IL-6) and Interlukin-23 (IL-23)), and oxidative stress parameters (Glutathione (GSH) and Malondialdehyde (MDA)) in a sample of Iraqi population. A total of 60 blood samples were collected from AS patients requited Rhe