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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: 2219
No. of views: 885638
No. of Crossref citations: 722
Publication Date
Sat Apr 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Antimicrobial Susceptibility of <i>Enterococcus</i> <i>faecium</i> Isolated from Bee-gut on <i>PhzM G</i>ene of <i>Pseudomonas aeruginosa</i> Isolates from Infected Wounds
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The aim of this study was to isolate and characterize Fructophilic lactic acid bacteria (FLAB) species from the honeybee gut. Based on the results of this study, it was found that the FLAB species obtained from honey were Gram-positive and catalase-negative, and this identification was confirmed through 16S rRNA gene sequencing. The researchers performed a primary screening to evaluate the effect of the cell-free supernatant (CFS) obtained from Enterococcus faecium (E5), and it was observed that the CFS showed a high inhibition zone of 23 mm against multidrug-resistant Pseudomonas aeruginosa, as determined by the agar well diffusion assay. This study also conducted further investigation to determine the optimal conditions for th

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Publication Date
Sat Apr 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Studying Periostin as a Diagnostic Marker in Sera of Iraqi Patients Hypothyroidism
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Hypothyroidism is one of the most common thyroid diseases in adults. Hypothyroidism is a condition that results from a deficiency of thyroid hormone and can range from being asymptomatic to life-threatening. A decrease in thyroid hormone production in the thyroid gland, a shortage of pituitary thyroid stimulating hormone, or a hypothalamic Thyrotropin-releasing hormone deficiency can cause hypothyroidism. Thyrotropin-releasing hormone deficiency Periostin is classified as both an extracellular matrix protein and a matricellular protein that belongs to the fasciclin family. As a matricellular protein, Postn plays a crucial role in the growth and maintenance of tissues and organs. Due to the limited research on the effects of Postn on the

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Publication Date
Sat Apr 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
An Approximate Solution for a Second Order Elliptic Inverse Coefficient Problem with Nonlocal Integral
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This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can have a l

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Publication Date
Sat Apr 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Calculating of the Electric Transition Forces and Radii of Even-even- Nuclei of Cadmium (<sup>100-124</sup><sub>48</sub><i>Cd</i> ) Cd Isotopes
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In the current research, the properties of even-even nuclei with a mass number (A≥100) for (100-12448Cd ) isotopes have been studied. This included distortion parameters () derived ,from an Intrinsic, electric, quadrupole, moments (0 )and deformation ,parameters  originate from a reduced ,

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Publication Date
Sat Apr 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Review of Consanguinity in the Iraqi Population: A Call to Action to Prevent a Future Health Catastrophe
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Although not uncommon worldwide, consanguinity has been a part of Arab culture and tradition as a means to strengthen tribal blood relations. However, this type of union has been linked to inherited diseases, particularly those of a recessive nature (e.g., hemoglobinopathies). Furthermore, several recent studies have documented highly significant associations between consanguineous parentage and common multifactorial diseases, including but not limited to hypertension, mental disorders, and several cardiovascular diseases. In Iraq, the prevalence of consanguinity is very high and still on the rise. This has resulted in an increased prevalence of inherited diseases and has significant negative impacts on Iraq’s limited economy. To addre

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Publication Date
Mon Apr 10 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Endophytic Fungi of Myrtle (Myrtus communis) and their Extracellular Enzyme Activity
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  The study was aimed to isolate and identify endophytic fungi from myrtle (Mrtus communis) leaves and study their extracellular enzymes activity. Results revealed isolation of 99 species or ioslated of endophytic fungi obtained from 500 leaves fragment, which represented colonization frequency (CF) of 20.4%. Those fungi were related to 23 species or isolates, Aspergilli were dominated over all species (11 species) with CF 14%. Moreover A. niger and A. flavus showed the higtest CF values over all. Other isolated fungi were related to the genera: Penicillium spp., Cladosporium sp., Cunninghamella sp., Derchslera sp., Alternaria sp. Paecilomyces sp. and sterile fungi (mycelia sterilia). Extracelluar enzymes activity showed varation in

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Cr (III), Fe (III), Co (II) and Cu(II)Metal ions complexes with azo compound derived from 2-hydroxy quinolin synthesis, characterization, thermal study and antioxidant activity
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Azo-ligand-(HL)([4-((2-hydroxyquinolin-3-yl)diazenyl)-N-(5-methylisoxazol-3-yl)benzenesulfonamide] ) ,  (2- hydroxy quinolin  derivative),reacts with the next metal ions (Cr (III), Fe (III),Co (II) and Cu(II))  forming stable complexes with unique geometries such as(tetrahedral for bothCo (II) and  Cu (II), octahedral for both Cr (III) and Fe (III)). The creation of such complexes was detected by employing spectroscopic means involving ultraviolet-visible which proved the obtained geometries, Fourier transfer proved the involvement of coordinated water molecule in all complexes besides the pyrolysis (TGA & DSC) studies proved the coordination of water residues with metal ions inside the coordination sphere as well as chlorine ato

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Strongly Pseudo Nearly Semei-2-Absorbing Submodules (II)
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Let  be a module over a commutative ring  with identity. Before studying the concept of the Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention the ideal  and the basics that you need to study the  concept of the Strongly Pseudo Nearly Semi-2-Absorbing submodule. Also, we introduce several characteristics of the Strongly Pseudo Nearly Semi-2-Absorbing submodule in classes of multiplication modules and other types of modules. We also had no luck because the ideal  is not a Strongly Pseudo Nearly Semi-2-Absorbing ideal. Also, it is noted that  is the Strongly Pseudo Nearly Semi-2-Absorbing ideal under several conditions, which is this faithful module, projective module, Z-regular module and content module and non-si

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Theoretical Study of The Influence of Donor Sensitize Dye on Performance of Dye-sensitized Solar Sells DSSCs
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    In this paper, a theoretical study was introduced to discussion the  Influence of donor senstizer on efficiency of solar cell with clear  focusing on dye senstized solar cell DSSCs applications was presented. Use of donor  as -sensitizer dye in solar cells was a viable contender in photovoltaics due to their spectrum of excited state to transfer more elkectrons to conduction band of semiconductor  .In this study, two systems Alq3/ZnO and D149/ZnO devices taken with same two solvents .Transtion energy ,coupling strength and transtion parameters are used to calculate the  electron current density , it  uses to calculate the photovoltic characteristic I-V ,fill factor and the efficiency of th

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Image Encryption Techniques Using Dynamic Approach : An Article Review
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In this study, a chaotic method is proposed that generates S-boxes similar to AES S-boxes with the help of a private key belonging to

In this study, dynamic encryption techniques are explored as an image cipher method to generate S-boxes similar to AES S-boxes with the help of a private key belonging to the user and enable images to be encrypted or decrypted using S-boxes. This study consists of two stages: the dynamic generation of the S-box method and the encryption-decryption method. S-boxes should have a non-linear structure, and for this reason, K/DSA (Knutt Durstenfeld Shuffle Algorithm), which is one of the pseudo-random techniques, is used to generate S-boxes dynamically. The biggest advantage of this approach is the produ

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Publication Date
Wed Mar 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectrophotometric Determination of Carbamazepine Via Oxidative Coupling Reaction with 2,4-dinitrophenyl hydrazine
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 An accurate and sensitive spectrophotometric method has been developed for the determination of carbamazepine (CRN.) in pure and dosage forms. The method is based on the oxidation of 2,4-dinitrophenylhydrazine (2,4-DNPHz) by potassium periodate than coupling with carbamazepine (CRN.) in alkaline medium to form a stable yellowish brown colored water-soluble dye with a maximum absorption at 485 nm. The variables that affect the completion of reaction have been carefully optimized. Beer’s law is obeyed over the concentration range of     (4-50 μg.mL-1) with molar absorptivity of (6.7335×103 L.mol-1.cm1). The limit of detection was (0.1052 μg.mL-1) and Sandell’s sensitivity value was 0.0350 μg.cm-2.

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Double-Exponential-X Family of Distributions: Properties and Applications
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A new family of distribution named Double-Exponential-X family is proposed. The proposed family is generated from the double exponential distribution. The forms of the probability densities and hazard functions of two distinct subfamilies of the proposed family are examined and reported. Generalproperties such as moment, survival, order statistics, probability weighted moments and quartile functions of the models are investigated. A sub family of the developed family of double –Exponential-X family of the distribution known as double-Exponential-Pareto distribution was used to fit a real life data on the use of antiretroviral drugs. Molecular simulation of efficacy of antiretroviral drugs is conducted to evaluate the performance of the

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Histological and Biochemical Effect of Galangin Conjugated Gold Nanoparticles on the kidneys Damage Induced by Carbon Tetrachloride of Adult Male Albino Mice
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This study aimed to determine histological and functional effects of Galangin (Gal) conjugated with Gold nanoparticles (AuNPs) on the Kidneys male albino mice treated with CCL4. Gold nanoparticles were prepared chemically by Turkevich Method. Characterizing of the prepared AuNPs and AuNPs+Gal was carried out using UV Spectrophotometry, X-Ray Diffraction (XRD) and particle size,. For the in vivo study, 42 adult male albino mice were used and randomly distributed into seven groups and experiment extended for 14 days, first group (G1) was control group without any treatment, (G2) group injected intra-peritoneal (i.p) with CCl4 once a week to the end of experiments, (G3)  injected with  AuNPs, (G4 and

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Theoretical Analysis Of The Photon Production Rate in the Quark-Gluon Interaction According To The Quantum Cromodynamic QCD Theory
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           In this work, we have used the QCD dynamic scenario of the quark gluon interaction to investigate and study photon emission theoretically based on quantum theory. The QCD theory is implemented by deriving the photon emission rate equation of the state of ideal QGP at a  chemical potential. The photon rate of the quark-gluon interaction has to be calculated for the anti up-gluon interaction in the g →  γ system at the temperature of system  with critical temperature ( 132.38, ,  and 198.57) MeV and photon energy (  GeV. We investigated a significant effect of critical temperature, strength coupling, and photon energy on the photon rate contribution. Here, the increased photon emission rate and decreased streng

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of substrate Nature on the properties of Tin Sulfide Nanostructured films Prepared by chemical bath deposition
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The substrate's nature plays an important role in the characteristics of semiconductor films because of the thermal and lattice mismatching between the film and the substrate. In this study, tin sulfide (SnS) nanostructured thin films were grown on different substrates (polyester, glass, and silicon) using a simple and low-cost chemical bath deposition technique. The structural, morphological, and optical properties of the grown thin films were investigated using X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), and ultraviolet-visible-near infrared (UV-Vis-NIR) spectroscopy. The XRD and FESEM results of the prepared films revealed that each film is polycrystalline and exhibits both orthorhombic and cubic stru

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Score for the Group SL(2,38)
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        The set of all (n×n) non-singular matrices over the field F. And this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension  over the field F, denoted by . The determinant of these matrices is a homomorphism from  into F* and the kernel of this homomorphism was the special linear group and denoted by  Thus  is the subgroup of  which contains all matrices of determinant one.

The rationally valued characters of the rational representations are written as a linear combination of the induced characters for the groups discussed in this paper. We find the Artin indicator for this group after studying the rationally valued characters of the rational

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis, Characterization and Biological Activity Study for Some New Metals Complexes with (3Z,3'E)-3,3'-(((2E,5E)-hexane-2,5-diylidene)bis(hydrazine-2,1-diylidene))bis(indolin-2-one)
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Our recent work displays the successful preparation of Schiff_bases that carried out between hexane-2,5-dione and 2 moles of (Z)-3-hydrazineylideneindolin-2-one forming in Schiff-bases-(L), Which in turn allowed combining with each of the next metal ions: (M2+) = Ni, Mn, Zn, Cu and Co forming complexes_ in high stability. The formation of resulting Schiff_ bases (L) is detected spectrally using LC_Mss which gave approximately matching results with theoretical incomes, 1HNMR proves the founding of doublet signal of (2H) for 2NH, FTIR indicates the occurrence of two interfered imine bands and UV-VIS mean is also indecates the formation of ligand. On the other hand, complexes-based-Schiff were characterized using the s

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Simulation and Analysis the Attenuation Effect of Atmospheric Layers on a Laser Beam Within the Visible Range
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Abstract: The power and the size of the final spot of the laser beam reaching the target are very important requirements in most of the laser applications and fields such as medical, military, and scientific, so studying laser propagation in the atmosphere is a very important topic. The propagation of the laser beam through the atmosphere is subject to several attenuation processes that deplete the power and expand the beam. Through the simulation results of the free electron laser within the visible region of the electromagnetic spectrum (400-700nm), it was found that the attenuation increases with decreasing wavelength. Laser propagation in the presence of rain and snow leads to a very large l

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Publication Date
Wed Mar 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Asteraceae ﺩﺭﺍﺳﺔ ﺑﺸﺮﺓ
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   ïº” ﻟﺴﺘﺔ ﺍﻧﻮﺍﻉ ﻣﻦ ﺍﻟﻌﺎﺋﻠﺔ ﺍﻟﻤﺮﻛﺒﺔ ،ﺍﺫ ﺩﺭﺳﺖ ﺧﻼﻳﺎ ﺍﻟﺒﺸﺮﺓ ﺍﻻﻋﺘﻴﺎﺩﻳﺔ ﺗﻨﺎﻭﻟﺖ ﺍﻟﺪﺭﺍﺳﺔ ﺍﻟﺤﺎﻟﻴﺔ ﺧﺼﺎﺋﺺ ﺑﺸﺮﺓ ﺍﻟﻮﺭﻗ ﻭﺍﻟﻤﻌﻘﺪﺍﺕ ﺍﻟﺜﻐﺮﻳﺔ ﻓﻲ ﻫﺬﻩ ﺍﻻﺟﺰﺍء ﻭﻟï

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Publication Date
Wed Mar 08 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Morphological and Histological Study of The Fore Brain (Cerebrum) In Quail Coturnix coturnix (Linnaeus, 1758)
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The morphological and histological aspects of fore brain (Cerebrum) in quail (Coturnix coturnix) have been investigated, results of the present study revealed that the cerebrum in quail is large size triangular shape, its surface contains folds of shallow grooves.      Microscopical examination declears that cerebrum consists of two regions, the first represents pallium which includes the external corticoid area which consist of hyperpallium and the dorsolateral corticoid area, it consists of piriform cortex and hippocampal complex. The second region is the internal corticoid areas dorsal ventricular ridge which contains the mesopallium, nidopallium and archopallium. he large size pyramidal neurons appeared in the nidopall

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Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method
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     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

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Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Employ Shrinkage Estimation Technique for the Reliability System in Stress-Strength Models: special case of Exponentiated Family Distribution
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       A reliability system of the multi-component stress-strength model R(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown  shape parameter α and known scale parameter λ  equal to two and parameter θ equal to three. Different estimation methods of R(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.

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Publication Date
Wed Jan 20 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study of Efficacy Adsorption of Methyl Green by Attapulgite and Modified Attapulgite Clay from Aqueous Solution
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    This paper includes the modification of the attapulgite  by precipitation of iron and aluminum compounds . Attapulgite (Atta) and modified attapulgite (Atta-m) clays are characterized by many  techniques ( FTIR , XRD ,SEM  with EDX ) .The  attapulgite clay before and after modification were used as the adsorbents for adsorption of methyl green (MG) . The results Indicate ,that the percentage of removal (MG) at equilibrium by using (Atta) and (Atta-m) clay were reached to  94% and 97% respectively. Indicating that the clay modification process was in addition to a relative improvement in the adsorption potential of the clay after modification.

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Publication Date
Mon Jun 17 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis and Structural Studies of Some Transition Metal Complexes of 5- phenyl-1,3,4 — Oxadiazole-2- thioethyl Carbanate
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 New complexes of cobalt (II). palladium (II). and platiniurn(H) with 5-phenyl- 1.3,4-oxadiazole-2- thioethylcarbanate (OXE) have been prepared and characterized by elemental analysis, 1R.L-V-Vis spectra. magnetic susceptipibility. and conductivity- measurements. Probable structures of the prepared complexes have been reported.

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Publication Date
Wed Apr 20 2022
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Modified Ranking Function to Compute Fuzzy Matrix Games
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     Game theory problems (GTP) frequently occur in Economy, Business Studies, Sociology, Political Science, Military Activities, and so on are some of the subjects covered. To tackle the uncertainty in Games, the analysis of games in which the payoffs are represented by fuzzy numbers (FN) will benefit from fuzzy set theory (FST).

The purpose of this paper is to develop an efficient technique for solving constraint matrix games (MG) with payoff trapezoidal fuzzy numbers (TFN). The description of the new ranking method is introduced for a constrained matrix with TFN and values. Stock market forecasting has been one of the most important research areas for decades. Stock market values are volatile, non-linear, complicated and ch

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Publication Date
Sun May 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Effect of Rifadin Drug on Lipids Metabolism of Rabbits
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  The aim of this study was intended to study the effect of rifadin drug on lipids metabolism  in the blood of the rabbits .Eight rabbits were used in the experiment ,they were divided into two groups ,first group(control group ) was administrated with 15mg/ml /day normal saline for 35 days ,while the second group (treated group )was administrated with (15/mg /kg/day) for 35 days of rifadin( capsule 300mg/kg).This study examined the influences of rifadin drug on the concentration of cholesterol  , triglycerides , HDL ,LDL and  VLDL in rabbits sera .The result showed that there were no significant  increased (p>0.05) in cholesterol concentration in rifadin  treated group compared with control group ,and th

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Publication Date
Thu May 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study of Antifungal Activity of Silbum marianum Extracts Against Some Species of Imperfect Fungi
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     This research was conducted to determine the effect of different concentrations of (milkthistle) Silbum marianum   leaves extracts on some plant pathogenic fungi included:      Fusarium oxysporum, Alternaria sp., and Botrytis cinerea.            Results showed the high antifungal activity of milk thistle leaves extract; this was evident at high concentration of extract (80) mg\ml, which completely inhibited the radial growth on solid media (PDA) for pathogens Fusarium oxysporum and Botrytis cinerea. While the spores of pathogen Alternaria sp. was able to  grow in all concentration which used in this study.  &n

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Publication Date
Thu Mar 09 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
New Schiff Base Derived From Folic Acid and 3Aminoacetophenone and its Metal Complexes with Some Transition Metals and Evaluation of Their Biological Activity
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 The ligand [Potassium (E)-(4-(((2-((1-(3-aminophenyl) ethylidene) amino)-4-oxo-1,4dihydropteridin-6-yl) methyl) amino)benzoyl)-L-glutamate] was prepared from the condensation reaction of folic acid with (3-aminoacetophenone) through Schiff reaction to give a new Schiff base ligand [H2L]. The ligand [H2L] was characterized by elemental analysis CHN, atomic absorption (A.A), (FT-I.R.), (U.V.-Vis), TLC, E.S. mass (for spectroscopes), molar conductance, and melting point. The new Schiff base ligand [H2L], reacts with Mn(II), Co(II), Ni(II), Cu(II), Cr(III) and Cd(II) metal ions and (2-aminophenol), (metal : derivative ligand : 2-aminophenol) to give a series of  new mixed complexes in  the general formula:- K3[M2(HL)(HA)2], (

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Publication Date
Sun Apr 20 2025
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Classification of Subsets of the Projective Line of Order Thirty Two and its Partitioned into Distinct Subsets
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The aim of this paper is to find the inequivalent k-sets in the finite projective line of order thirty-two, PG(1,32). The number of projectively distinct 4-set is five and all of them are of type N(neither harmonic nor equianharmonic). The k-sets, k=4,…,11 have been done, where the number of projectively distinct are 5,11,53,148,481,1240,2964,6049, respectively. The k-sets k=12,..,17 classified depending on the projectively distinct 11-sets whose have non-trivial subgroups only, where the numbers of projectively distinct are 493,5077,2583,288,2412,697. The stabilizer group of each k-sets is computed. The kind of groups that computed for the k-sets are I, Z_2, Z_3, V_4, S_3, Z_2×Z_2×Z_2, Z_2×Z_2×Z_2×Z_2 and the large group is the d

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Publication Date
Sun Aug 01 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Novel Heuristic Approach for Solving Multi-objective Scheduling Problems
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    In this paper, we studied the scheduling of  jobs on a single machine.  Each of n jobs is to be processed without interruption and becomes available for processing at time zero. The objective is to find a processing order of the jobs, minimizing the sum of maximum earliness and maximum tardiness. This problem is to minimize the earliness and tardiness values, so this model is equivalent to the just-in-time production system. Our lower bound depended on the decomposition of the problem into two subprograms. We presented a novel heuristic approach to find a near-optimal solution for the problem. This approach depends on finding efficient solutions for two problems. The first problem is minimizing total completi

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