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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: 2018
No. of views: 769115
No. of Crossref citations: 624
Publication Date
Mon May 15 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Study Structural and Electrical Properties of Hg0.5Pb0.5-xSbxBa2Ca2Cu3O8+ δ Superconductors
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  Mercury-lead-antimony based superconductors with the formula Hg0.5 Pb0.5xSbxBa2Ca2Cu3O8+δ (x=0, 0.10 and 0.15) have been prepared by useing three step solid state reaction processes. Electrical resistivity, using four probe technique, is used to find the transition temperature Tc. It is found from that sample Hg0.5 Pb0.5Ba2Ca2Cu3O8.437 is semiconductor , sample Hg0.5 Pb0.4Sb0.1Ba2Ca2Cu3O8.353 is normal state with metallic behaviors, while sample Hg0.5 Pb0.35Sb0.15Ba2Ca2Cu3O8.233 is superconducting state with critical transition temperature (Tc) is 126K. X-ray diffraction (XRD) analysis showed a tetragonal structure with decrease in the c-axis lattice constant for the samples doped with Sb as compared with these which have no Sb

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Publication Date
Sun May 14 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A New Design of Fractal Optical Modulation
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In this paper it was designed a new fractal optical modulation by using a new iteration of fractal function, the result was analyzed by MTF evaluation, and it compared with results of normal optical modulation.

The normal and fractal optical modulator is a circular disc which has a radius R=9cm, both of them consist of twenty sectors, ten sectors are opaque and the other ten sectors are transmitted for the light.

      The fractal optical modulator contains two patterns, the pattern two can be used to detect the target, and pattern one can be used to lock the target

The best similarity of MTF behavior for normal and fractal Reticle was evaluating the power transparent depends on the size o

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Study of Some Growth of Two Hyborids of Tomato Plant (Lycopersicon Esculentum Mill.) Grown Under The Influence of Sodium Chloride in The Nutrient Solution and Proline Spraying to Shoot.
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The experiment was conducted inside a glasshouse at the Department of Biology/
Education college Ibn- Alhaitham/ Baghdad University during the growing season 2010-2011. The aim of the study was to assess the influence of increasing of NaCl concentration in
the nutrient solution and different concentrations of proline as spray on the vegetative growth
on the chlorophyll content, soluble carbohydrates percentage, flowers number and the proline
content of vegetative growth. The aim of this study was also to determine the satiable
concentration of proline while decrease the injerion. Effect of NaCl on the studied traits of
two hyborids of tomato plants namely Olga F1 and Hymar F1. Sodium chloride concentration
of 0

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Publication Date
Sat Sep 23 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Charact'erizatio.n of new Schiff base ligand [(2-{1-[(2 hydraxy­ benzylidene)-hydrazono]-ethyl} benzene-I, 3, 5--triol.] and it's CQmp.lexes. with Co en\ Ni . (U),, c·u(U)' and · zn(II).
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The eaction  of 2 4 .6-trihydroxyactophenonemonohydra1e  with

l hydr.azine monohydrate was realized ti·nder reflu.(( in methanol and i:l.

Jew drops of glacial acetic acid we.re added to give lhe'(int rmediate)

2-(1hydr pno-ctbyt)-benzcne-·1.3.5-r:Qql,       which      reacted     wittl

saEcy.laldehyde. jn methm)ql to gjy;e 'a new :tyRe CNzOi) Ligand  (H:flL]

f(2-{1-[(2-=bydroxy-bertzylide·ne)-bydrazqoo,J-e·thy.1}bcnze·neJ ;3·,5

of

 

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Effect of CCl4 and Nigella sativa oil on histological changes of liver in the immature white Rats
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This study aimed to investigat the effect of Carbon tetrachloride CCl4 and Nigella
sativa oil on histological changes of liver. It was used only (20) immature male rats. to study
the effect of Carbon tetrachloride CCl4 and Nigella sativa oil on changes. The rats were
randomly divided into equal groups as follows. First group was injected intra dermally with
0.1 ml, normal saline (two times per weeks). This group was considered as control group .The
second group was injected intra dermally with (Carbon tetrachloride CCl4 ml / 100g ) of body
weight for ( two times per weeks was injected for (8weeks) . The third group It was orally
given 0.1 ml dose of Nigella sativa oil, it was injected for (8weeks).The fourth g

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of Variety , Gibberellic Acid And NPK Fertilizer and their Interactions On Absorption and Transport Rates of Some Macronutrient Elements in Chamomile plant
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This experiment was carried out in the field of botanical garden which belongs to Biologi
Department , College of Education (Ibn Al-Haitham), University of Baghdad during the
growing season 2009-2010.The experiment was designed to study the effect 5 concentrations
of Gibberellic acid(GA3)( 25,50,75,100and125mg.L
-1
) and 2 levels of NPK (17:17:17)
fertilizer (200 and 400 Kg.ha
-1
) and their interaction on the rates of absorption and transport
of some macronutrient elements in two varieties of chamomile plant ( Local variety ,
Matricaria chamomilla L. and German variety , Matricaria recutitia L.) . Randomized
Complete Block Design (RCBD) was used with 3 replicates for each treatment .Control plants

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Viscosity and Density of Chrom Alum in Aqueous Poly (Ethylene Glycol) Solution at Different Temperature
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   Density data of  alum chrom in water and in aqueous solution of poly (ethylene glycol) (1500) at different temperatures (288.15, 293.15, 298.15) k have been used to estimate the apparent molar volume (Vθ), limiting apparent molar volume (Vθ˚) experimental slope (Sv) and the second derivative of limiting partial molar volume [δ2 θ v° /δ T2] p .The viscosity data have been analyzed by means of Jones –Dole equation to obtain coefficient A, and  Jones – Dole coefficient B, Free activation  energy of activation per mole of solvent, Δμ10* solute, Δμ20* the activation enthalpy ΔH*,and entropy, ΔS*of activation of viscous flow. These results have been discussed

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
In Vitro Antimicrobial Activity of Thymus Vulgaris,Origanum Vulgare and Rosmarinus Officinalis Against Dental Caries Pathogens
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The in vitro antimicrobial activity of Thymus vulgaris,Origanum vulgare and
Rosmarinus officinalis water extracts were studied against Streptococcus mutans,
Lactobacillus acidophilus and Candida albicans isolates two of each isolate. All cold water
extracts exhibited antimicrobial activity against all tested microorganisms. The largest zone of
inhibition was obtained against Candida albicans isolates. Streptococcus mutans isolates and
one isolate of Lactobacillus acidophilus showed no effect in 300mg\ml concentration of
Thymus vulgaris extract,while the same concentration of Rosmarinus officinalis extract had
no effect on all Streptococcus mutans isolates and Lactobacillus acidophilus isolates
.Origanum vul

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectral Study of the Pollutants ( Gelbstoff) in Water Liquefaction of Some areas of Baghdad Province by Using the Technique of Raman, Flora
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  In this research we study one of the pollutants(Gelbstoff ) such as Humic  and Fulvic Acids  in tap waters by using the technique of  Raman, Flora to some regions of Baghdad , the results appear that the tap waters  were pollutants which know yellow substance or Gelbstoff instant of suspending waters, which appear through the scattering of the incident light to same the wave length of Raman ,also calculate Raman shift which was 3640 cm-1 and force constant to band (O – H ) was 743 N/m, where the peak of Raman was at the wave length 441 nm after used the excitation wave length 380 nm . The results were in an agreement with lectures [8][9][10].

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Publication Date
Mon May 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study to the Main Effects on the Auger de-excitation Transition
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  An Eigen-state expansion method is applied to the transition of the Auger de-excitation charge transfer (AD) process in the interaction between clean Cu,Al and Na surfaces and excited incident gases H and He .We use this method to describe the effective surfaces electronic structure. It's shown that the AD efficiency is deeply influenced by the presence of the energy band for the surfaces and the potential energy stored within the excited incident atom, thus for long interaction time we use a slowly atom's about 1KeV to scatter from metals surfaces where the electron couldn't probe the metal band structure and Za the surface - projectile distance. Also we drive a new formula for AD interaction Matrix element

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Detection of Bacteria Causing Burn Infection Isolated from Several Hospitals in Baghdad
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The results of the present study showed that twenty-five samples were collected for the age group 35–40 years and four samples for the age group 65–70 years for both genders. The results showed that 48 (48%) of the samples were obtained from the hands, 16 (16%) from the legs, 12 (12%) from the abdominal area, and 10 (10%) from the chest area. The four (4%) samples were obtained from burns in the back and thighs area. The samples taken according to the cause of burns were 40 (40%) due to hot water, hot liquids, or hot steam, followed by 18 (18%) due to the use of hot tools, 15 (15%) due to fires, 12 (12%) due to electric currents, 10 (10%) due to chemicals such as strong acids, alkaline lye, paint thinner, or gasoline, and 5 (5%) due

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Crossref
Publication Date
Mon Apr 24 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectrophotometric Determinations of Sulfacetamide Following Simple Diazotization and Coupling with Chromotropic Acid
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A simple, sensitive, accurate and economic spectrophotometric method has been developed for the determination of sulfacetamide (SFA) in pure form, synthetic sample and urine. The method is based on diazotization of primary amine group of sulfacetamide with sodium nitrite and hydrochloric acid followed by coupling with chromotropic acid in alkaline medium to obtain a stable orange colored chromogen which exhibit a maximum absorption (λmax) at   511.5 nm. Different variables affecting the completion of reaction have been carefully optimized following the classical univariate sequence and  modified simplex method (MSM). Under optimized conditions, Beer’s law obeyed in the concentration range of (0.5-  &nbs

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Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Design of Electrostatic Unipotential Lens Accelerating And Decelerating Operated Under Finite And Infinite Magnification Conditions
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  Theoretical study computerized has been carried out in field electron optics , to design electrostatic unipotential lens , the inverse problem is important method in the design of electrostatic lenses by suggesting an axial electrostatic potential distribution using polynomial function. The paraxial –ray equation is solved to obtain the trajectory particles that satisfy the suggested potential function. In this research , design electrostatic unipotential lens three-electrode accelerating and decelerating L=5 mm operated under finite and infinite magnification conditions. The electrode shape of the electrostatic lens was then determined from the solution of the Laplace's equation's. the results showed low values of spherica

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Publication Date
Fri Apr 21 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Comparative Biochemical Study of Interleukin -35 and Some Sex Hormones in MS Female Patients with Duration of the Disease*
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    Multiple sclerosis (MS) is a chronic disorder of the central nervous system (CNS) characterized by autoimmune inflammation, demyelination, and axonal damage. The present study aimed to shed a light on the contribution of interlukin-35 and its relation to some sex hormones in the pathogenesis of multiple sclerosis. Sixty six female patients with age range (20-40) years were taken from Baghdad Teaching Hospital through the period from Nov. 2012 to –April 2013 and 20 apparently healthy subject as control group matched age as group G1. The patients were divided into three groups depending on duration of MS diseases G2 from 3 months to 2 years, G3 from 2 years to 4 years, G4 from 4 years to 10 years and more. Investi

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Publication Date
Wed Apr 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Estimation of Serum Malondialdehyde and Uric acid levels in Smokers and non-Smokers
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  Malondialdehyde (MDA) is one of many low molecular weight end-products of lipid peroxidation; it is as an index of lipid peroxidation. Uric acid is one of the endogenous oxidant-antioxidant paradoxes.        The aim of this study is to evaluate the levels of serum MDA and uric acid in smokers and non smokers.  This study was carried out from January to July 2012 on (30) smokers and (30) non smokers. Serum MDA level was measured spectrophotometrically using thiobarbituric acid method, whereas serum uric acid was measured using enzymatic colorimetric method.      The results of the study revealed a significant increase (P<0.001) in uric acid value in smokers subject

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Publication Date
Wed Apr 12 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Optical Properties of Aluminum Doped CdO Thin Films Prepared by Vacuum Thermal Evaporation Technique
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   In this work, thin films of undoped and Al-doped CdO with (0.5, 1 and 2) wt.%  were prepared by using thermal vacuum evaporation on glass substrate at room  temperature. The optical absorption coefficient (α) of the films was determined from transmittance spectra in the range of wavelength (400-1100) nm. The spectral transmission and the optical energy band gap decrease from 75% and 2.24 eV to 20%  and 2.1 eV respectively depending upon the Al content in the films, also our studies include the calculation of  the optical constants (refractive index, extinction coefficient, real and imaginary part of dielectric constant) as a function of photon energy.  It is evaluated that the optical band gap of

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Publication Date
Mon Apr 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of Power He-Ne Laser on Growth of Dermatophyte Trichophyton mentagophytes
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This study aims to evaluate the effect of low power a semi-conductor He-Ne laser 4 mw power with 635 nm length on the growth and cell viability of dermatophyte Trichophyton mentagophytes. For this study, skin samples of 22 patents were collecting; those patients were suffering from dematophytsis caused by the dermatophytes, three isolates were diagnosed in dermatophytes group were T. mentagophytes.  Results showed that rays of semi-conductor laser with 635 nm wavelength of 4 mn power have affected the fungal growth T. mentagophytes (the ideal isolates) in sold media when exposed to laser radiation in different periods of 10-20 second duration, but the other two isolates gave negative results. The effects of He-Ne laser rays in dry w

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Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis And Characterization Of New Metals Complexes Of [N-(acetyl amino) Thioxomethyl] Valine
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A new ligand [N-(acetyl amino) thioxomethyl] valine was prepared from the reaction of acetyl iso thiocyanate with valine. The ligand was characterized by FT-IR, UV- vis and 1HNMR spectrum, The complexes with some metal ions (M +2 =Co,Ni,Cu,Zn,Cd,Hg) have been prepared and characterized. The structural diagnosis were established by IR,UV-Vis  spectrum, flame atomic absorption spectroscopy conductivity and magnetic susceptibility ,the complexes showed tetrahedral geometry around the metal   l.

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Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study Of Optimum Conditions For The Removal Of Ruthenium And Cerium Using Freshly Prepared Manganese Dioxide
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 The adsorption of Ru and Ce were carried out using manganese dioxide as adsorbent. The Optimization of the adsorption conditions were studied as a function of shaking time, nitric acid, metal ions, concentrations and temperature effects.      A rapid initial adsorption on MnO2 is followed by a steady and slow increase of metal uptake. The equilibration time is reached after four hours shaking for Ru and Ce and    the adsorption is much better from one molar acidic solution and 90°C.

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Publication Date
Mon Apr 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Simulation Expirment for Proofing the Theoretical Assumption of Time Complexity for Binary Search Tree
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      It is frequently asserted that an advantage of a binary search tree implementation of a set over linked list implementation is that for reasonably well balanced binary search trees the average search time (to discover whether or not a particular element is present in the set) is O(log N) to the base 2 where N is the number of element in the set (the size of the tree).  This paper presents an experiment for measuring and comparing the obtained binary search tree time with the expected time (theoretical), this experiment proved the correctness of the hypothesis, the experiment is carried out using a program in turbo Pascal with recursion technique implementation and a statistical method  to prove th

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Publication Date
Mon Aug 07 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Preliminary Pharmacological Evaluation of Some New Triazole Derivatives
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  On the basis of the results which was previously obtained from the structural and the theoretical studies on ~-adrenergic drugs, a series of 2-propanolamine derivatives containing triazole moiety have been prepared and evaluated for their cardiovascular activity . These derivatives were tested by using spontaneously-beating right atria of albino rats.

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Publication Date
Mon Aug 07 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Characterization of Tetradentate Complexes Type N2O2 From the Reaction of 2-Hydroxy -1, 2-Diphynel-Ethanone Oxime [H2L] With Mn II, Fe II, Co II, Ni II, Cu II and Hg II Ions
...Show More Authors

       Tetradentate complexes type [M (HL) 2] were prepared from the reaction of 2-hydroxy -1, 2-diphynel-ethanone oxime [H2L] and KOH with ( Mn II, Fe II, Co II, Ni II , Cu II and Hg II ), in methanol with (2:1) metal: ligand ratio. The general formula for Cu II and Mn II complexes are [M (HL) 2 Cl.H2O] K, for Co II [Co (HL) 2. H2O] and [M (HL) 2] for the rest of complexes. All compounds were characterised by spectroscopic methods, I.R, U.V-Vis, H.P.L.C, atomic absorption and conductivity measurements chloride content. From the data of these measurements, the proposed molecular structures for Fe II and Hg II complexes are tetrahedrals, while Mn II and Cu II complexes are octahedrals, Ni II complex adopting

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Publication Date
Mon Aug 07 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study the Effect of Rifampicin in the Level of Thyroid's Gland Hormones and Thyroid - Stimulating Hormone in Rabbits
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The aim of this study was intended to study the effect of rifampicin in the level of thyroid's gland hormones (T4 ØŒT3) and thyroid -stimulating hormone (TSH) in rabbits.            Eight male rabbits were used through out this study, their weights were measured before the starting of the experiment. Animals were divided into two groups (each group contains 4 rabbits), the first group was administrated daily with 15 mg/Kg physiological normal saline for 35 days and used as a control group, while the second group was administrated with 15 mg /Kg daily for 35 day of rifampicin capsule 300 mg.       At the end of the experiment, all of animal groups were

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Publication Date
Mon Sep 18 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Estimation of Ceruloplasmin activity, and copper, iron levels in ·sera of nor1nal pregnants
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This  study  was undertaken  to shed light on the changes  of levels of CP

activity, Cu and  Fe in sera of .(53) normaJ non-smoker pregnant's  without complication, during  three1rimestcrs of pregnancy.

G1  inc.l_ude  (I 8) pre nants in  the 1' 1 tri nester, G2 19)  pret:,rp:all.ts  _wear

taken     m the  2"    tnmester  and  G3  (16) pregnants  m the  3rd  trunester.

/\nothe.r ('18) ·serum samples were taken from liealthy non-pregnant wqmen

age matched as control·group G4.

Results bowed a significant steady  elevation in CP .p:ctivity and &n

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Publication Date
Wed Apr 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of Aqueous Extract and Essential Oils of the Leaves of Eucalyptus incrassate on β- Lactam Resistant Staphylococcus aureus
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According to the extraction procedure , Eucalyptus incrassata leave sample yielded 5% and 2% w/w(Based on dry leaves ) of the aqueous extract and essential oils respectively. Disk diffusion method was used to determine the antimicrobial activity of aqueous extract and essential oils of E . incrassata leaves against eight isolates of multidrug- resistant of Staphylococcus aureus ( S. aureus) . It was found that aqueous extract and essential oils have variable antimicrobial activity(the inhibition zone diameter ranged from 7 to 14 mm respectively ) , while essential oils showed more effect than aqueous extract .         It was noticed that values of Minimal Inhibitory Concentration ( MIC )  for

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Publication Date
Mon Apr 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of Camel Milk &Urine in Viability of Entamoeba histolytica Growing in Culture Media LEM
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   This study included the isolation of the parasite Entamoeba histolytica from bloody mucoid diarrhea specimens of patients suffering from amoebic dysentery and cultivation of parasite in Locke-egg medium (LEM) to study  the effect of camel's milk and urine on the viability of E . histolytica with different concentrations (1 , 5  and 10 % ). The ability of camel's milk and urine in inhibiting the E . histolytica viability  is examined after  24 and 48 h of incubation The results showed that the activity of camel's milk and urine was  directly proportional  with  the increase  in concentration and incubation period. Since the  highest rate of parasite death reached ( 99.5% and 99.4%

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Publication Date
Wed Aug 09 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Effect of Ascorbic Acid on Pathogenic Staphylococcus aureus Growth singly and in Combination with Some Antibiotics
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 One hundred and fifteen isolates of Staphylococcus aureus were isolated from human infected wound and burn. The resistance of this organism for eight commonly used antibiotics was determined by disc diffusion methods.          The minimum inhibitory concentration MIC was determined for each drug by tube dilution method. Results showed significant variations in the MIC values. It was found that two isolates had high resistance for the eight antibiotics used. Effect of ascorbic acid on bacterial growth was studied singly and in combination with antibiotics. Reductions in MIC value were reported for different antibiotics when tested by growth curve method too. 

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Publication Date
Mon Sep 18 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Protein bound fucos, protein bound hexose and total calcium in sera of patient with thyroid dysfunction and control
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Protein bound fucose (PBF), protein  bound hexose (PBHex), and total calcium {T.Ca) were 'determined in sera of (40) hy-p.ertnyroidism , (40)  hypothyroidism patients and (40) controL The resultsr vealed  a significant decrease in the kwel of PBF,  PBHex and T.Ca in sera of patients with .hyperthyroidism  compared  to control; Inc se Qf PBF. there nQ difference in its level betwe.en patients with hypothyroidism and  control  group.  While there  is a significant increment in  PBHex leveli:n both hyper and hypothyroidism With respect to that of control Result  indicates, that total calcium levels were i.n  the nomml range for all p tients groups. Patient  compa

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Publication Date
Wed Apr 19 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study the Effect of Zn Doping in the Structural and Electrical Properties of CdTe Thin Films
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Some of structural ,and electrical properties of pure and zinc (Zn) doped cadmium telluride thin films with impurity percentages (0.5, 1, 1.5)%, deposited on hot glass substrate (temperature equals to 423K) of  thickness of 300nm and rate deposition of 0.5 nm.s-1  by thermal co-evaporation technique under vacuum of (2×10-5)Torr have been investigates. The structural properties for the prepared films were studied before and after. doping process by analysis of the X-ray diffraction, and it appeared that pure and dopant  CdTe thin films are polycrystalline and have the cubic structure with preferential orientation in the [111] direction, and the crystal structure of the films were improved due to doping process. From d.c

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Publication Date
Wed May 03 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Designing Feed Forward Neural Network for Solving Linear VolterraIntegro-Differential Equations
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The aim of this paper, is to design multilayer Feed Forward Neural Network(FFNN)to find the approximate solution of the second order linear Volterraintegro-differential equations with boundary conditions. The designer utilized to reduce the computation of solution, computationally attractive, and the applications are demonstrated through illustrative examples.

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