This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th

Two specie's of terrnitls are described as new to science from Iraq Amitermes corpnlentus sp. n. and Anacanthotermes savvensis sp. n., with two figures.

1,3,4-oxadiazole-5-thion ring (2) successfully formed at position six of 2-methylphenol and five of their thioalkyl (3a-e). Furthermore 6-(5-(Aryl)-1,3,4-oxadiazol-2-yl)-2-methylphenol (5a-i) were formed at position six by two method. The first method was from cyclization their corresponding hydrazones (4a-e) of 2-hydroxy-3-methylbenzohydrazide (1) using bromine in glacial acetic acid. The second method was from cyclization the hydrazide with aryl carboxylic acid in the presence of phosphorusoxy chloride. The newly synthesized compounds were characterized from their IR, NMR and mass spectra. The antioxidant properties of these compounds were screened by 2,2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) assay

1, 3, 4-oxadiazole-5-thion ring (2) successfully formed at position six of 2-methylphenol and five of their thioalkyl (3a-e). Furthermore 6-(5-(Aryl)-1, 3, 4-oxadiazol-2-yl)-2-methylphenol (5a-i) were formed at position six by two method. The first method was from cyclization their correspondinghydrazones (4a-e) of 2-hydroxy-3-methylbenzohydrazide (1) using bromine in glacial acetic acid. The second method was from cyclization the hydrazide with aryl carboxylic acid in the presence of phosphorusoxy chloride. The newly synthesized compounds were characterized from their IR, NMR and mass spectra. The antioxidant properties of these compounds were screened by 2, 2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) a

The research tacklets the role of risks arising from the excessive use of derivative contracts for trading in financial crises, including the recent global financial crisis in (2008) which is known the mortgage crisis.

   In order to prove the hypothesis of the research, the risk index of derivative contracts has been chosed as expressed in the measure of (value at risk) to be the main field for testing the hypothesis of research. The duration of the contract  has been also chased  for (15) years between the years (2001- 2015), the period preceding the global financial crisis, while the second represents the period of time that followed. The research reached a number of conclusions, bu

In the present study a series of some four-,five-and seven-membered heterocyclic compounds have been synthesized by the reaetion of Schiff bases (1a,b) with chloroacetyl chloride, sodium azide, thioglycolic acid or various anhydrides to give azetidinone (2a,b), tetrazole (3a,b), thiazolidinone (4a,b) and 1,3-oxazepine derivatives (5-8a,b) respectively. Schiff bases (1a,b)were prepared from the reaction of p-toluidine with aromatic aldehydes. All synthesized compounds were characterized by physical properties and spectral data.

New series of Schiff bases 2(a-j) and corresponding beta-lactam derivatives 3(a-j) were synthesized from cefalexin (1) as starting material. The compound (1) was reacted with different aldehydes and ketones to give Schiff bases derivatives 2(a-j). The synthesized Schiff bases were cyclized by chloroacetyl chloride in the presence of triethylamine to form beta-lactam derivatives 3(a-j). The compounds were characterized by deremination melting point, FT-IR and 1H NMR. The beta-lactam derivatives were screened in vitro antibacterial against some bacterial species

The sol-gel route using an agar gel with calcium nitrate and phosphate solution as starting materials for producing hydroxyapatite (HAP). The product formed were needle like, zigzag and straight fibres. The fibrous products on sintering transformed into stoichiometric HAP with a biological Ca/P ratio of 1.67. The influences of pH, temperature, nature of base and phosphate solution on the growth of fibrous HAP were studied. The pH of the solution was found to greatly influence the growth rate and morphology of the resultant product. The optimum gel temperature was found to be 60oC and sintering temperature of 900oC for 1 hour. The crystalline, thermal, functional and morphological characteristics of the fibrous HAP were investigated.