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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
Sun Jul 01 2018
Journal Name
International Journal Of Engineering Research And Management
The first and Second Order Polynomial Models with Double Scalar Quantization for Image Compression
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Publication Date
Wed Apr 08 2020
Journal Name
Periodicals Of Engineering And Natural Sciences
Bayes estimators for reliability and hazard function of Rayleigh-Logarithmic (RL) distribution with application
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In this paper, we derived an estimators and parameters of Reliability and Hazard function of new mix distribution ( Rayleigh- Logarithmic) with two parameters and increasing failure rate using Bayes Method with Square Error Loss function and Jeffery and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived of Bayesian estimator compared to the to the Maximum Likelihood of this function using Simulation technique by Monte Carlo method under different Rayleigh- Logarithmic parameter and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator in all sample sizes with application

Publication Date
Mon May 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Removal Interferences with Spectrophotometric Study for the Determination of Chromium, Vanadium and Their Application
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  The species of Cr (III), Cr (VI) in biological samples and V(IV), V(V) in foods & plants samples were determined by spectrophotometric methods. Integrated spectral studies of complexes [Cr (III, VI)-DPC], [Cr (VI)-bipy], [VO-SH], [V (V)-8-HQ] which included a study of the optimum conditions for the complexes formation by the investigation of the chemical and physical variables affecting each complex formation, the nature of complexes, the preparation of calibration curves of the complexes and treated the resulted data by modern statistical methods and study the interfering species. Interferences were removed to explain the reactions thermodynamically by determining Eï‚°cell, Keq. and ∆G values and includes a study of

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Publication Date
Sat Nov 01 2014
Journal Name
International Journal Of Statistics
Single and Double Stage Shrinkage Estimators for the Normal Mean with the Variance Cases
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Publication Date
Thu Aug 31 2023
Journal Name
Journal Of Kufa For Mathematics And Computer
Four Points Block Method with Second Derivative for Solving First Order Ordinary Differential Equations
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Publication Date
Wed Aug 19 2020
Journal Name
Applied Water Science
Spiral path three phase fluidized bed reactor for treating wastewater contaminated with engine oil
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Abstract<p>In this study, a new type of circulating three-phase fluidized bed reactor was conducted by adding a spiral path and was named as spiral three-phase fluidized bed reactor (TPFB-S) to investigate the possibility for removing engine oil (virgin and waste form) from synthetic wastewater by using Ricinus communis (RC) leaves natural and activated by KOH. The biosorption process was conducted by changing particle diameter in the range 150–300 and 300–600 µm, liquid flow rate in the range 2.5–4.5 L/min and gas flow rate in range of 0–1 L/min, while other parameters initial oil emulsion concentration, pH, adsorbent concentration, agitation speed and contact time were kept constant at 2000 mg/L, 2,</p> ... Show More
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Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
Synthesis of ZnS Quantum Dots for QDs-LED hybrid device with different cathode materials
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Publication Date
Mon Apr 03 2023
Journal Name
International Journal Of Online And Biomedical Engineering (ijoe)
An Integrated Grasshopper Optimization Algorithm with Artificial Neural Network for Trusted Nodes Classification Problem
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Wireless Body Area Network (WBAN) is a tool that improves real-time patient health observation in hospitals, asylums, especially at home. WBAN has grown popularity in recent years due to its critical role and vast range of medical applications. Due to the sensitive nature of the patient information being transmitted through the WBAN network, security is of paramount importance. To guarantee the safe movement of data between sensor nodes and various WBAN networks, a high level of security is required in a WBAN network. This research introduces a novel technique named Integrated Grasshopper Optimization Algorithm with Artificial Neural Network (IGO-ANN) for distinguishing between trusted nodes in WBAN networks by means of a classifica

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Publication Date
Mon Sep 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On Double Stage Shrinkage Estimator For the Variance of Normal Distribution With Unknown Mean
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     This paper is concerned with preliminary test double stage shrinkage estimators to estimate the variance (s2) of normal distribution when a prior estimate  of the actual value (s2) is a available when the mean is unknown  , using specifying shrinkage weight factors y(×) in addition to pre-test region (R).

      Expressions for the Bias, Mean squared error [MSE (×)], Relative Efficiency [R.EFF (×)], Expected sample size [E(n/s2)] and percentage of overall sample saved of proposed estimator were derived. Numerical results (using MathCAD program) and conclusions are drawn about selection of different constants including in the me

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Publication Date
Sun Jul 02 2017
Journal Name
Journal Of Educational And Psychological Researches
The dimensions forMarzano of learning and its relation with crisis management for teachers Kindergartens
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importumt educational institution as (kindergartens) need teachers which qualified ownes modalities in their education for children , as Marzanu method in a way of learning and own methods of crisis management, because the teachers that own those styles of learning ginekindergarten children knowledge and the childrenIeaving based on theMeaing and knowledge and integration of their information, And teachers that earn methods of crisis management provide for the children of the kindergarten security within the educational institution which in turn affect the growth and development of the Child and then abilities, health physical, mental, psychological …etc.., The aims of the current research have identified to recognize: 1- the dimension

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