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Ibn AL-Haitham Journal For Pure and Applied Sciences College of Education for Pure Science / Ibn AL-Haitham
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ISSN: 1609-4042
eISSN: 2521-3407
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No. of publications: 2189
No. of views: 1445434
No. of Crossref citations: 722
Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis, Characterization and Studying the Enzyme Activity of New Benzothiazole Schiff Base Ligand (HL) and Its Complexes with Some of Metal Ions
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    A new heterocyclic Schiff bases ligand (HL) derived from condensation of 2-Amino-4-methylbenzothiazole with 4-Diethylaminosalicylaldehyde have been synthesized and characterized by (FTIR & UV.Vis) spectroscopies, (1H & 13C)NMR spectra, mass spectrum, elemental microanalysis (C,H,N,S). Metal complexes with Co(II), Ni(II), Cu(II), Zn(II) and Cd(II) ions have been also synthesized and characterized by (FTIR & UV.Vis) spectroscopies, flame atomic absorption, molar conductivity measurements and magnetic susceptibility. These studies indicate that the mole ratio (L:M) is (2:1) for Co(II) complex and (1:1) for other complexes. The spectral results indicate that the ligand coordinates with met

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study the Levels of Glucagon Like Peptide-1(GLP-1) and Related Parameters in Iraqi Hyperlipidemia Patients with Diabetes Mellitus.
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     The glucagon-like peptide-1 is secreted by intestinal L cells in response to nutrient ingestion. It regulates the secretion and sensitivity of insulin while suppressing glucagon secretion and decreasing postprandial glucose levels , additionally, glucagon-like peptide-1 delays gastric emptying and suppresses appetite. The impaired secretion of glucagon-like peptide-1 has negative influence on hyperlipidemia, diabetes  and insulin resistance related diseases the levels of its secretion change with the intake of different nutrients. Some drugs also have influence on GLP-1 secretion .

 

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis of Some New Heterocyclic Fused Rings Compounds Based on 5-Aryl-1,3,4-Oxadiazole
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The work includes synthesis and characterization of some new heterocyclic compounds, as flow: The compound (3) (5-(4-chlorophenyl) -2-hydrazinyl-1,3,4-oxadiazole was synthesized by using two methods; the first method includes the direct reaction between hydrazine hydrate 80% and 5-(4-chlorophenyl)-2- (ethylthio) 1,3,4-oxadiazole (1), the second method involves converting 5-(4-chlorophenyl)-1,3,4-oxadiazol-2-amine (2) to diazonium salt then reducing this salt to compound (3) by stannous chloride. Compound (3) was used as starting material for synthesizing several fused heterocyclic compounds. The compound 6-(4-chlorophenyl)[1,2.4] triazolo [3,4,b][1,3,4] oxadiazole-3-(2H) thione (compound 4) was synthesized from the reaction of compound (

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectrophotometric Determination of Cefotaxime via Diazotization Reaction in Pure and Pharmaceutical Samples
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      An accurate and sensitive spectrophotometric method has been developed for the determination of cefotaxime (CEF) in pure and pharmaceutical samples. The suggested method depended on the coupling reaction between diazotized cefotaxime and 3,5-dimethyl phenol (3,5-DMPH) in basic medium to form light orange, water soluble dye, that is stable and has a maximum absorbance at 497nm. The calibration graph was liner over the concentration range (1-70) µg.mL-1 with LOD of 0.750 µg.mL-1 and LOQ of. 2.740 µg. mL-1, sandal sensitivity of 0.0526 µg. cm-2 . molar absorptivity 11328 Lmol-1 cm-1 . The stoichiometry composition was found by Jobs a

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Publication Date
Fri Sep 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A study of Geomagnetic Field and It's secular variation at the Location Brazilian Anomaly (25°S, 45°W).
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ln this paper we study  and  analysis  the  total intensity  (P) .and the horizontal  component (H) of the geomagnetic field at the location na ly Brazilian    Anomaly  (Lat   25S,    long   4S·"W)    in  which   the geomagnetic field intensity  has a minimum  value. We examine the relationship. between  the { F , H) with altitude  at a certain latitude, and

.relationship  between  ( F,H ) with  the latitude  at  the certain  altitude

.We study  also  the nature  of the secular  variation  of the

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Publication Date
Tue Sep 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The biotic influence of biological insecticide ( Agerin) and plant growth regulator ( Match ) on the first larvae instar of spiny boll worm Earias insulana(Boisd.) (Lepidoptera:Phalaenidae)
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First  instar  larvae    of  spiny  cottcn  boll  wonn   Earias insulana

(Bosid.)    were    Fed     on    different    concentrations    of    biological insecticides (Agerin) and growth  regulators (Match) for ( 5, 3 and one days) .The results showed  that Agerin at 1.5 giL caused   99.9 , 99.9. and  96.9  %  accumulative killing  percentages  while    0.5  g/L  of  this biological  insecticidt::s resulted  in  92.96 , 58.9 and 33.3% in the three periods  of  feeding  

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Publication Date
Tue Sep 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Palm Leaf as a Thermal Insulation Material
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This paper presents calculat,ion of thermal conductivity (K) of palm

leaf  experimentally  using  Lee s  disc  method   to  be  used  as   thermal

insulator. The therma l conducti vity is found to be equal to (k=0.03W/mK)

indicating  that  palm l eaf is a good thermal  insulator com pared to the other insulators. The effect of the thermal insulator   thickness  on temperature di lTt::rence,  heat   transfer    coefficient,   thermal     conductance,   thermal resistance,  thermal  insulation are in vestigated in this paper. It was  found that

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Publication Date
Tue Sep 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Calculation For Multipole Mixing Ratios OF Gamma Transitions From Deformation Levels IN 152Sm Nucleus
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In the  present  work  , the a2 - ratio  method  has  been used  to calculate the multipole mixing  ratios , 5 - values • of y - transitions from excited levels of deformation  nucleiL-. ( 152Sm ) .

The results obtained confirm the validity of this method in calculating the o - values .

The  present  results are in good  agreement  with  those  of the experimental  results,   ref.( I ,2)  , and   of  theoretical   results   using interaction  boson model (IBM-I) ,ref. (5).

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Publication Date
Sat Sep 23 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Characterisation of Novel Cobalt(li),Copper (II) and Mercury (II) Complexes of Poly Vinyl Urethanised Oxime.
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The reaction  of poly (vinyl  alcohol) (PV A) with Urea in (DMSO)

resulted  in uerthanised oxim, wr,ich reacted with diacetylmonoxime  in a (DY.ISOfmethanol) to give anew type (N2) polymeric bidentate imine oxime ligand [HL], The ligand was reacted with MCh (where M= Co, Cu, and Hg). Under  reflux in a (DMF/Methanol) mixture with (I:1) ratio to give Complexes  of the general formula [M (T.)2]X, (where M=

Co,Hg,  Cu). All .:ompouncs have been characterized  by spectroscopic

methods  [IR,  U.V.-Vis, A tomi<;absorption] microanalysis along with conductivity measurements, from  the  above::  data the proposed molecular structure for Co,Cu, and Hg is a

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Publication Date
Thu Dec 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis, Characterization and Study of Mesomorphic Behavior of New Bent and Liner Core Compounds Containing Heterocyclic
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  We described herein the synthesized and characterized of new bent and liner core compounds containing thiazolidin-4-one ring[XI-XIII] and [XIV-XVI] respectively. These compounds synthesized by sequence reactions starting from reaction resorcinol or hydroquinone with chloracetyl chloride to yield compounds [I] and [II] ,then the later compounds reactant with 4-hydroxybenzylaldehyde to product dialdehyde compounds [III] and [IV] .The Schiff bases compounds[V-VII] and [VIII-X] synthesized from reaction the compound [III] or [IV] with different aromatic  amines, while the bent and liner core mesogens containing thiazolidin-4-one ring [XI-XIII] and [XIV-XVI] synthesized from reaction Schiff bases compounds[V-VII] or  [VIII-X]

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Publication Date
Thu Dec 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Adsorption of Tetracycline on the Bauxite and Modified Bauxite at Different Temperatures
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  In this study, bauxite and modified bauxite /polymer, which were prepared as an adsorbent surfaces to adsorption of the tetracycline from aqueous solutions. A series of adsorption experiments were conducted to determine the equilibrium time and temperature effect on the adsorption process. The results showed that adsorption was agreed with the Freundlich equation model for the surface of the bauxite. As for the modified bauxite surface, the results were consistent with the Langmuir equation model. The values of the basic thermodynamic functions of the adsorption process were calculated, so the process of adsorption was founded   spontaneous and endothermi

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Publication Date
Thu Dec 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Characterization of FeІІ , CoІІ , NiІІ , CuІІ and ZnІІ Complexes With Dithiocarbamate and N-Donor Ligands
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New complexes of first series of transition metals with P-amino benzene dithiocarbamate of the general formula [M(PABdtc)2] and [ M(PABdtc)2(L)n] M=Fe( ІІ ),Co( ІІ ),Ni( ІІ ) ,Cu(ІІ) and Zn (ІІ). PABdtc = Paraamino benzene dithiocarbamate ,n=2 when  L= Py,É£-Pic,iso qunoline ,3,5lutidine  n=1when L=1,10-phenanthroline, en, 2,-2bipy.and the type(R)4N[Ni(PABdtc)3] R= methyl, ethyl are prepared. Physico chemical characterization of these complexes was applied  using magnetic susceptibility measurements, molar conductance , Infrared and electronic spectra, Metal content measurements, molar conductance indicate complexes of the type [M(PABdtc)2] and [M(PABdtc)2(L)n] are non-electrolyte

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Publication Date
Thu Dec 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Fluorescence, Biological Activity and Spectroscopic Studies of Azo-linked Schiff Base Ligand Type (ONO) and Its Complexes with CrIII, CoII NiII and CdII Ions
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 The precursor [W] [2-(2-(naphthalen-5-yl) diazenyl)-4-amino-3-hydroxynaphthalene-1sulfonic acid] was synthesized from reaction of diazonium salt with 1-amino-2-naphtol-4sulfonic acid. Then the tridentate Schiff base ligand type ONO was synthesized from the reaction of the precursor with salicyaldehyde in 1:1 mole ratio to produce the ligand H2L [2-(2-(naphthalen5-yl) diazenyl)-4-(2-hydroxynaphthalen-3-yl)methyleneamino)-3-hydroxy salicyalene-1-sulfonic acid],the reaction achieved in methanol as a solvent under reflux. Spectroscopic methods IR, U.V, 1H,13C-NMR was used to characterize the ligand. Complexes of [CrIII, CoII, NiII and CdII] ions were also prepared through reaction of ligand with metal salts in 2:1 mole ratio at reflux,

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Publication Date
Sat Jan 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Assessment of Monocyte Chemoattractant Protein -1 and Fertility Hormones in Iraqi Women with Polycystic Ovarian Syndrome
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Polycystic ovarian syndrome (PCOS) is a well-known endocrinopathy and one of the most frequent endocrine-reproductive-metabolic syndromes in women, which can result in reduced fertility. While the actual cause is unknown, PCOS is regarded as a complicated genetic characteristic with a great degree of variability. Moreover, hormones and immune cells, including both innate and acquired immune cells, are thought to interact in PCOS. Chronic low-grade inflammation raises the risk of autoimmune disease. The study's purpose is to investigate the chemokine monocyte chemoattractant protein-1 (MCP-1) and fertility hormones in samples of women patients with polycystic ovary syndrome (PCOS) in the City of Medicine. Sixty PCOS women comprise 30 heal

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Evaluation of CRP, IL-6 and Calprotectin in Saliva of Patients Suffering From Crohn’s Disease (CD)
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Inflammatory bowel disease (IBD) a chronic inflammatory condition of the gastrointestinal tract characterized by alternating episodes of clinical relapse and remission  (Wallace, 2014), with Crohn's disease (CD) and ulcerative colitis (UC) being the two primary subtypes  (Souza, 2016).  The present study was achieved in Baghdad teaching hospital from November 2021 to June  2022 to prove if the diagnostic marker of Crohn’s disease (CD) (IL-6, CRP and Calprotectin( are rises in saliva as in sera and if there are significant difference in the levels of those markers between the Crohn’s disease (CD)group and control group.

The recent study was measured the levels of C-reactive protein (CRP), Interleukin-6 (IL6

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Gas Sensitivity Properties of Nano Ferrite CuxAl0.3-XNi0.7Fe2O4 Synthesized by Sol-Gel Method
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This study includes the preparation of the ferrite nano ferrite CuxAl0.3-XNi0.7Fe2O4 (where: x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) M using the auto combustion method (sol-gel), and citric acid was used as fuel for auto combustion. The ferrite samples were checked by X-ray diffraction (XRD), Field Emission Scanning Electron Microscopes (FE-SEM), and energy dispersive X-ray analyzer (EDX). They showed that the prepared compound has a face-centered cubic structure (FCC). The lattice constant increases with an increase in the percentage of doping of the copper ions, and a decrease for the aluminum ion and that the compound is porous and its grains are spherical, and there are no other

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
New Green Modalities of Flow Injection Technology for Assaying Anti-Allergic Drugs in Pharmaceutics and Biological Samples
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A new approach and the developed FIA technique with many advantages (economic, fast, simple, accurate, and high throughput) are used to determine the decongestant drugs (Phenylephrine.HCl, Oxymetazoline.HCl) in biological samples, pharmaceutical formulations, and pure samples via continuous flow injection technique by oxidative coupling reaction, where the method depends on the interaction of the decongestant drug with organic reagents to produce colored compounds, where Phenylephrine reacts with 4-AAP at λmax503 nm to produce a red compound, and the Beer’s law range of 10-600 μg.mL-1 . As for Oxymetazoline, it reacts with DNPH at λmax 631nm to produce a green compound with a linear dynamic range of

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Publication Date
Sat Jan 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of Partial Substitution of Ge-S-Cd Alloys on the Density of Energy States
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Five samples of the ternary alloy Ge-S-Cd were created using the melting point method, and the effects of partially substituting cadmium for germanium were determined. and partial substitution of germanium by cadmium was used to study the change in electrical conductivity. Electrical experiments were performed on Ge35-xS65Cdxternary alloy with x = 0, 5, 10, 15, and 20. It was discovered that the conductivity (σdc) rises with rising temperature in all samples under experiment. This confirms that the samples have semiconductor behavior. It has been observed that there are three regions of electrical conductivity in the electrical conductivity curve at low, moderate, and high temperatures. The pr

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Publication Date
Mon May 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field
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     The objective of this paper is, first, study a new collection of sets such as field and we discuss the properties of this collection. Second, introduce a new concepts related to the field such as measure on field, outer measure on field and we obtain some important results deals with these concepts. Third, introduce the concept of null-additive on field as a generalization of the concept of measure on field. Furthermore, we establish new concept related to - field noted by weakly null-additive on field as a generalizations of the concepts of measure on and null-additive. Finally, we introduce the restriction of a set function  on field and many of its properties and characterizations are given.

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Publication Date
Mon May 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Application of Iterative Method for Solving Higher Order Integro-Differential Equations
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The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

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Publication Date
Fri Sep 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Ability of kaolin clays in Adsorption of Toluene 0-Nitro Toluene and 2,4-Dinitro Toluene Part 1
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This  study was concerned with the adsorption of Toluene ,0·

nitro Toluene and 2,4.dinitro Toluene on The surface of kaolin clay.

The  adsorption isotherms  were of types( S3,S4 ) according  to Giles classification and were in a good correlation with Freundlich equation  in the range of cuncenlraliuns studied. The re5ult indicated that adsorption capacity increase with the increase of equilibrium concentration. The effect of the nwnber of substituted nitro groups in the adsorption extent of toluene was found to decrease in the following order:·

Toluene   > 2,4-dinitro toluene  > 0-nitro toluene

Adsorption on  kaolin surface were examined as afunction

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Publication Date
Sat Sep 23 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
E·voiution of Topology and Wei,ght-s. of Neural Netwo·rks. Using.Semi Genetic Operators
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Evolutionary·co.nipimit'iQo  is  a· c'!a s of glbbal ·searb  techniq

based on the lei.lffi:ing process ,of  g po_pl)'latiog-·of pote.n:tiaf solutions to

a  ven probl_e-ID'.  thahas .been  succe_ssfull'y  applied    19  v ety of

prQblern, lll thls paper a riew approach  to. design lie_ ural ne'twQj:ks

based oh ev.ohltipnary -computa.tio.rt i·s pre.Seri-L  _A   tine-f.!£ clurP.mosome

'repr:esentati:on  or the etwor}< i_s.  u_secl: 'Q.y  genetiC  gperntb_l:s, whicQ

allow th¢  voJution of.the   chitecture and' weight-s Â

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Combining a Hill Encryption Algorithm and LSB Technique With Dispersed Way for Securing Arabic and English Text Messages Hidden in Cover Image
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         In this paper a hybrid system was designed for securing transformed or stored text messages(Arabic and english) by embedding the message in a colored image as a cover file depending on LSB (Least Significant Bit) algorithm in a dispersed way and employing Hill data encryption algorithm for encrypt message before being hidden, A key of 3x3 was used for encryption with inverse for decryption, The system scores a good result for PSNR rate      ( 75-86) that differentiates according to  length of message and image resolution

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Approximate Solution for Fuzzy Differential Algebraic Equations of Fractional Order Using Adomian Decomposition Method
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      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

 

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Algorithm to Solve Linear Volterra Fractional Integro-Differential Equation via Elzaki Transform
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       In this work, Elzaki transform (ET) introduced by Tarig Elzaki is applied to solve linear Volterra fractional integro-differential equations (LVFIDE). The fractional derivative is considered in the Riemman-Liouville sense. The procedure is based on the application of (ET) to (LVFIDE) and using properties of (ET) and its inverse. Finally, some examples are solved to show that this is computationally efficient and accurate.

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Publication Date
Thu Nov 02 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Determination of Magnesium, Zinc, and Reduced Glutathione Levels in Serum of Asthmatic Patients
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Asthma  is a disease  characterized by hyper reactivity  of the trachea and   bronchi   to  reversible   either   spontaneously  or  as  a  result   of treatment.

In this study serum magnesium,  Zinc, and reduced glutathione  levels

were  meas ured  in  order  to  determine   their  levels  in  the  asthmatic patients and comparing  these levels with healthy controls.

Fifty-  four  asthmatic   patients  were  enrolled  in  the  study  and  had their pulmonary  function test, and the levels of Mg,Zn

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Publication Date
Fri Sep 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Comparism between phospholipase activity in (Candida albicans) by use two substrates (lecithin, L-a-phosphatidyl inositol)
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Comparative study on tb.e activity of phospholipase enzyme which is produced by yeastØ¢  cum/ida albicansØ¢  Ø¢ into different culture media that contain phospholipids as substrates. The agar containing substrate (L-aآ­ phosphatidyl inositol) was used .

The agar containing lecithin as other substrate for comparision was also

used.

The second culture media was found the best for enzyme activity which

was measured by precipitation zone .

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Publication Date
Sat Jan 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Review using continuous flow injection analysis technique in the determination of several drugs
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Continuous flow injection analysis (CFIA) is one of the simplest, easiest, and multilateral analytical automation methods in moist chemical analysis. This method depends on changing the physical and chemical properties of a part of the specimen spread out from the specimen injected into the carrier stream. The CFIA technique uses automatic analysis of samples with high efficiency. The CFIA PC compatibility also allows specimens to be treated automatically, reagents to be added, and reaction conditions to be closely monitored. The CFIA is one of the automated chemical analysis methods in which a successive specimen sample is to be estimated and injected into a vector stream from a flowing solution that meets the reagent and mixes at a spe

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Publication Date
Sat Jan 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Effect of Mycorrhizal Inoculation and Fertilization with Plant Residues on the Growth of Chard Plant
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In order to study the effect of inoculation with mycorrhiza and fertilization with plant residues on the growth of plants, we used two factors: the first two levels of mycorrhiza inoculation, Glumus mossea (0 and 10 g.pot-1) and the second factor, four levels of plant residues (10 g.pot-1) celery plant residues, 10 g pot-1 mint residues, and 10 g pot-1 black bean seed residues. Mychorrizal treatment (10 g pot-1) increased the number of mycorrhiza spores and the infection percentage of mycorrhizal by 917.44% and 13088.23%, respectively; celery treatment (10 g.pot-1) increased the chlorophyll index in the leaves and height of the chard plant by 31.34% and 94.04%, re

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Publication Date
Sat Jan 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Comparison of Complex Sadik and KAJ Transforms for Ordinary Differential Equations to the Response of an Uncompressed Forced Oscillator
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In this paper we have presented a comparison between two novel integral transformations that are of great importance in the solution of differential equations. These two transformations are the complex Sadik transform and the KAJ transform. An uncompressed forced oscillator, which is an important application, served as the basis for comparison. The application was solved and exact solutions were obtained. Therefore, in this paper, the exact solution was found based on two different integral transforms: the first integral transform complex Sadik and the second integral transform KAJ. And these exact solutions obtained from these two integral transforms were new methods with simple algebraic calculations and applied to different problems.

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