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Statistical Properties of Second Iteration of Logistic Map
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This paper introduces a novel non-classical probability distribution, termed the Logistic Map distribution, which is constructed by transforming a polynomial function derived from the second iteration of the logistic map. The logistic map a well-known discrete-time dynamical system has been extensively employed in diverse scientific domains, including population dynamics (to model bounded growth under environmental constraints), physics (to study nonlinear dynamics and deterministic chaos), and economics (to represent complex, nonlinear patterns in financial and economic time series). The proposed distribution is fully characterized by two parameters: a scale parameter and a shape parameter, with the constraint ensuring the non-negativity and integrability of the density. Within this valid parameter space, we rigorously derive and establish a comprehensive suite of statistical properties. These include the probability density function, cumulative distribution function, reliability (survival) function, and hazard (failure rate) function. Furthermore, we obtain analytical expressions for key descriptive measures such as the mode and median, as well as for higher-order characteristics including the moment generating function, factorial moment generating function, and characteristic function. The proposed distribution most closely application field in materials science specifically, the statistical modeling of particle or grain size distributions in industrial powder processing, metallurgy, and pharmaceutical manufacturing. The primary objective of this study is to formalize a new family of probability distributions grounded in the mathematical framework of dynamical systems, specifically leveraging the logistic function commonly encountered in differential and difference equations. By doing so, we bridge concepts from nonlinear dynamics and classical statistical theory. The secondary aim is to conduct a thorough investigation of the distribution’s mathematical structure and statistical behavior, thereby establishing its potential utility for modeling bounded, non-negative random phenomena in applied fields such as reliability engineering, survival analysis, and environmental statistics.

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Publication Date
Fri Jan 11 2019
Journal Name
Iraqi Journal Of Physics
Effect of water absorption on some mechanical and physical properties of epoxy/polyurethane blend reinforced with nano silica powder
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The aim of this work is to evaluate some mechanical and physical
properties (i.e. the impact strength, hardness, flexural strength,
thermal conductivity and diffusion coefficient) of
(epoxy/polyurethane) blend reinforced with nano silica powder (2%
wt.). Hand lay-up technique was used to manufacture the composite
and a magnetic stirrer for blending the components. Results showed
that water had affected the bending flexural strength and hardness,
while impact strength increased and thermal conductivity decreased.
In addition to the above mentioned tests, the diffusion coefficient
was calculated using Fick’s 2nd law.

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Publication Date
Tue Feb 01 2022
Journal Name
Journal Of Physics And Chemistry Of Solids
Effect of Sr/Mg co-substitution on corrosion resistance properties of hydroxyapatite coated on Ti–6Al–4V dental alloys
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This study assessed the effect of co-substitution of strontium (Sr) and magnesium (Mg) ions into the hydroxyapatite (HA) coating which was deposited on Ti–6Al–4V dental alloys by an electrochemical deposition process. The deposited layers were examined using energy-dispersive X-ray spectroscopy, scanning electron microscopy, Fourier transform infrared spectroscopy, atomic force microscopy and X-ray diffraction. The corrosion behavior of Ti–6Al–4V alloys in an artificial saliva environment was studied through potentiodynamic polarization technique and electrochemical impedance spectroscopy. The results indicated that the substituted Sr and Mg ions in HA improved the HA coating, where the protection efficiency percentage (PE%) for Ti

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Publication Date
Wed Sep 01 2010
Journal Name
Materials & Design
Influence of glass addition and sintering temperature on the structure, mechanical properties and dielectric strength of high-voltage insulators
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Publication Date
Tue Jul 01 2025
Journal Name
Journal Of Building Engineering
Impact of low NaOH molarities on mechanical and durability properties of ambient and oven-cured fly ash geopolymer concrete
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Publication Date
Sun Jan 01 2023
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees22fr
Preparation and study the partial substitution of aluminum with copper on some physical properties of the compound TlSr2Ca2Cu3O8+δ
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Publication Date
Thu May 01 2025
Journal Name
International Journal Of Engineering
Impact of Using Polyethylene Polymer on Properties of Hot Asphalt Mixture by Conducting Semi-Wet and Dry Mixing Process
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In recent years, various methods have been developed to enhance the characteristics of asphalt pavement in order to face the continuous challenges of increasing traffic loads and changing climate conditions. One of the most popular and successful methods is modifying the asphalt mixtures or asphalt binder with the addition of polymers. Therefore, two types of Polyethylene (PE) polymer, High-Density PE (HDPE) and Low-Density PE (LDPE), are used in this research. Two methods were applied to prepare PE-modified asphalt mixtures: Semi-Wet Method (S-WM) and Dry Method (DM). The findings of the investigation indicated that the addition of PE polymer can reduce the wear loss of aggregate. In general, the experimental results revealed that asphalt

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Publication Date
Thu Jun 30 2022
Journal Name
International Journal Of Drug Delivery Technology
Evaluation of Antibacterial and Cytotoxicity Properties of Zinc Oxide Nanoparticles Synthesized by Precipitation Method against Methicillin-resistant Staphylococcus aureus
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A novel technique for nanoparticles with a chemical method and impact for resistance bacteria methicillin-resistant Staphylococcus aureus (MRSA), UV-visible analysis confirmed the by Fourier transform infrared spectroscopy (FT-IR) and Energy dispersive X-Ray (EDX), Scanning electron microscope (SEM) and X-ray diffraction pattern estimation antimicrobial excellent antibacterial activity against MRSA (with zone of inhibition of 11 ± 02 mm , 9 ± 01 mm,8 ± 03 mm and 7.5 ± 02 mm and 6.5 ± 02 mm) at different concentrations (0.5 ,0.25, 0.125, 0.0625, 0.03125) mg/ml while good activity was 16 ± 03 mm at 17 ± 02 mm zone at 0.25, 0.125 mg/mL, respectively. The increase in microorganism resistance to antibiotics a couple of have caused

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Publication Date
Sun Sep 01 2024
Journal Name
Iraqi Journal Of Physics
Physical Properties Studies of Magnesium Phthalocyanine (MgPc) Thin Films of Different Annealing Temperatures Prepared by Pulsed Laser Deposition Technique
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Magnesium Phthalocyanine (MgPc) was deposited on a glass substrate by pulsed laser deposition (PLD) using Q-Switching Nd:YAG laser with wavelength 1064 nm, repetition rate 6 Hz, at room temperature (300K) and different annealing temperatures (373, 473, and 573)K under vacuum condition of 10-3 torr. All films were annealed for one hour to attain crystallinity. X-ray diffraction (XRD) of MgPc powder indicated that MgPc crystallizes in polycrystalline with a monoclinic structure. While comparing the MgPc films, it was observed that the intensity of the characteristic peak increases with temperature, and the crystallization exhibited a monoclinic structure typical of the β-form. The Miller indices, hkl, values for each diffraction peak

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Publication Date
Fri Jul 01 2011
Journal Name
Engineering And Technology Journal
Off-Line Arabic Signature Recognition Based on Invariant Moments Properties
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Publication Date
Mon Jan 01 2024
Journal Name
Nonlinear Functional Analysis And Applications
NEW SEVEN-PARAMETER MITTAG-LEFFLER FUNCTION WITH CERTAIN ANALYTIC PROPERTIES
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In this paper, a new seven-parameter Mittag-Leffler function of a single com-plex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

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