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Zernike Polynomiales· for Opticl Ssytew. With Borizantal Recta_nguJar Aperture
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For  small   aberrations,  the  Â·suehl'  ratio of  an . im i'ng syStem

  • depends on trne aberration v·ariance. Its· aberration fu.nct1on ·is e:qJanded in terms 9f-l nike polynomials. which are_ oirrh6goilal over a circular apeltitte. Their advane Uejn the    f;:l t tbat they call be icl.eritified. witl·c1a:s.sh::aj. abe,ttati{)ns 'balanced to jield  minimum varia,.o_q,and

thuS maximum St:rehl  t"a;tio. [n r«enr pap-er, we derived Cl<lse4 .fonn or

Zmike   polyhotnials  that  ate  orthonormal  over "- horizontal rect'angul'ar pupil'. (p.anil.lel to· the >Htxi.es) with ar'€a equal 1t.  Ustng the circle pO:lynomials as the · basis functions. f(;)r  th:ehl- onb.ogonalization

p_ver  such   pupil,    we: ;derive   closed-foim  polyr.wmials   that   are ortbonormaJ  over   rectangular  pupil  by us ng,  Gram-sl1m.it  method These· polynomials,  we unique in that they  rue_ not  <:>nly  orthogonal

acrossuch- pupils,. but aJ:so -re.present balanced -classicl aberrations,

just as tbe Zemike ·circlpolyiiornials are unique in- these respects but

also repr sent balanced dasskal  aberration$.

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Publication Date
Fri Aug 20 2021
Journal Name
Open Access Macedonian Journal Of Medical Sciences
Autogenous Onlay Graft with Compression Plate for Treatment of Persistent Humeral Shaft Aseptic Non-union with Failed Previous Surgery
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BACKGROUND: The humeral shaft fractures have a good rate of union, despite this fact, still there is a significant rate of nonunion after nonoperative treatment and more often after operative treatment. AIM: The aim of the study is to evaluate the autogenous onlay graft with compression plate for treatment of persistent humeral shaft non-union with failed previous surgery both radiological and functional outcome. MATERIALS AND METHODS: A prospective study on twenty patients having persistent aseptic non-union age between 20 and 60 years old, after failed surgical treatment of fractures humeral shaft in Al-Zahra teaching and Al-Kindy teaching hospitals, while infected nonunion, diabetes mellitus, secondary metastasis, smoking, a

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Publication Date
Fri Apr 04 2025
Journal Name
Journal Of Physical Education
Special Endurance And its Relationship With 10 Km Walking Achievement for Youth
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Publication Date
Mon Dec 05 2022
Journal Name
Baghdad Science Journal
K-Nearest Neighbor Method with Principal Component Analysis for Functional Nonparametric Regression
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This paper proposed a new  method to study functional non-parametric regression data analysis with conditional expectation in the case that the covariates  are functional and the Principal Component Analysis was utilized to de-correlate the multivariate response variables. It  utilized the formula of the Nadaraya Watson estimator (K-Nearest Neighbour (KNN)) for prediction with different types of the semi-metrics, (which are based on Second Derivative and Functional Principal Component Analysis (FPCA))  for measureing the closeness between curves.  Root Mean Square Errors is used for the  implementation of this model which is then compared to the independent response method. R program is used for analysing data. Then, when  the cov

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Publication Date
Mon May 15 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Finite Difference Method for Two-Dimensional Fractional Partial Differential Equation with parameter
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 In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.

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Publication Date
Sun Jan 14 2018
Journal Name
Journal Of Engineering
Regression Modeling of EDM Process for AISI D2 Tool Steel with RSM
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In this paper, Response Surface Method (RSM) is utilized to carry out an investigation of the impact of input parameters: electrode type (E.T.) [Gr, Cu and CuW], pulse duration of current (Ip), pulse duration on time (Ton), and pulse duration off time (Toff) on the surface finish in EDM operation. To approximate and concentrate the suggested second- order regression model is generally accepted for Surface Roughness Ra, a Central Composite Design (CCD) is utilized for evaluating the model constant coefficients of the input parameters on Surface Roughness (Ra). Examinations were performed on AISI D2 tool steel. The important coefficients are gotten by achieving successfully an Analysis of V

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Publication Date
Mon Jun 19 2023
Journal Name
Journal Of Engineering
EXPERIMENTAL AND THEORETICAL INVESTIGATIONS FOR BEHAVIOR OF PRECAST CONCRETE GIRDERS WITH CONNECTIONS
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This research presents experimental and theoretical investigation of 15 reinforced concrete spliced and nonspliced girder models. Splices of hooked dowels and cast in place joints, with or without strengthening steel plates were used. Post-tensioning had been used to enhance the splice strength for some spliced girders. The ANSYS computer program was used for analyzing the spliced and non-spliced girders. A nonlinear three dimensional element was used to represent all test girders. The experimental results have shown that for a single span girder using steel plate connectors in the splice zone has given a sufficient continuity to resist flexural stresses in this region. The experimental results have shown that the deflection of hooked do

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Publication Date
Tue Dec 01 2015
Journal Name
Journal Of Economics And Administrative Sciences
Ant Colony Optimization Algorithm for Design of Distribution System with Practical Application
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The Ant System Algorithm (ASA) is a member of the ant colony algorithms family in swarm intelligence methods (part of the Artificial Intelligence field), which is based on the behavior of ants seeking a path and a source of food in their colonies. The aim of This algorithm is to search for an optimal solution for Combinational Optimization Problems (COP) for which is extremely difficult to find solution using the classical methods like linear and non-linear programming methods. 

The Ant System Algorithm was used in the management of water resources field in Iraq, specifically for Haditha dam which is one of the most important dams in Iraq. The target is to find out an efficient management system for

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
peridos for transversal coincidence maps on compact manifolds with a given cohomology
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Publication Date
Fri May 01 2020
Journal Name
Journal Of Engineering
Thermal Efficiency for Passive Solar Chimney with and Without Heat Storage material
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In this study, a different design of passive air Solar Chimney(SC)was tested by installing it in the south wall of insulated test room in Baghdad city. The SC was designed from vertical and inclined parts connected serially together, the vertical SC (first part) has a single pass and Thermal Energy Storage Box Collector (TESB (refined paraffin wax as Phase Change Material(PCM)-Copper Foam Matrix(CFM))), while the inclined SC was designed in single pass, double passes and double pass with TESB (semi refined paraffin wax with copper foam matrix) with selective working angle ((30o, 45o and 60o). A computational model was employed and solved by Finite Volume Method (FVM) to simulate the air i

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Publication Date
Fri Jul 26 2019
Journal Name
Dental Materials Journal
Semi-interpenetrating network composites reinforced with Kevlar fibers for dental post fabrication
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