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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
Thu Aug 29 2024
Journal Name
Materials
Experimental Study to Investigate the Performance-Related Properties of Modified Asphalt Concrete Using Nanomaterials Al2O3, SiO2, and TiO2
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The dual nature of asphalt binder necessitates improvements to mitigate rutting and fatigue since it performs as an elastic material under the regime of rapid loading or cold temperatures and as a viscous fluid at elevated temperatures. The present investigation assesses the effectiveness of Nano Alumina (NA), Nano Silica (NS), and Nano Titanium Dioxide (NT) at weight percentages of 0, 2, 4, 6, and 8% in asphalt cement to enhance both asphalt binder and mixture performance. Binder evaluations include tests for consistency, thermal susceptibility, aging, and workability, while mixture assessments focus on Marshall properties, moisture susceptibility, resilient modulus, permanent deformation, and fatigue characteristics. NS notably im

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Publication Date
Fri Jun 26 2026
Journal Name
Journal Of Baghdad College Of Dentistry
The effect of adding single walled carbon nanotube with different concentrations on mechanical properties of heat cure acrylic denture base material
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Background: The most widely used material for fabrication of denture base is poly methyl methacrylate, despite its popularity, the main problems associated with it as a denture base material are poor strength particularly under fatigue failure inside the patient mouth, impact failure outside the patient mouth, which are the main causes for fracture of denture, several studies was done to increase mechanical properties of denture base. The present study was conducted to evaluate and compare the effect of addition single walled carbon nanotubes in different concentrations to polymethyl methacrylate on some mechanical properties (surface hardness, surface roughness, impact strength and transverse strength). Materials and methods: Forty eight

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Publication Date
Fri Sep 09 2022
Journal Name
Journal Of Ovonic Research
The effects of CuO doping on structural, electrical and optical properties of CdO thin films deposited by pulsed laser deposition technique
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Thin films of (CdO)x (CuO)1-x (where x = 0.0, 0.2, 0.3, 0.4 and 0.5) were prepared by the pulsed laser deposition. The CuO addition caused an increase in diffraction peaks intensity at (111) and a decrease in diffraction peaks intensity at (200). As CuO content increases, the band gap increases to a maximum of 3.51 eV, maximum resistivity of 8.251x 104 Ω.cm with mobility of 199.5 cm2 / V.s, when x= 0.5. The results show that the conductivity is ntype when x value was changed in the range (0 to 0.4) but further addition of CuO converted the samples to p-type.

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Publication Date
Mon Oct 03 2022
Journal Name
Physica Scripta
Radiation shielding properties of Cd-Bi-Pb-Zn-borate glasses: influence of Bi<sub>2</sub>O<sub>3</sub> activation
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Abstract<p>We report the detail characterizations and <italic>γ</italic>-radiation protecting characteristics of some new types of cadmium (Cd)-bismuth (Bi)-lead (Pb)-zinc (Zn)-borate glasses of the form (70-x)B<sub>2</sub>O<sub>3</sub>-10ZnO-10PbO-10CdO-xBi<sub>2</sub>O<sub>3</sub> (with x = 0 to 20 mol%) synthesized via melt-quenching process. The influence of various Bi<sub>2</sub>O<sub>3</sub> contents on the <italic>γ</italic>-radiation shielding traits of the obtained glass samples was evaluated by exposing them at different <italic>γ</italic>-ray energies (0.356, 0.662, 1.173, and 1.33 MeV) whic</p> ... Show More
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Publication Date
Tue Oct 25 2022
Journal Name
Aip Conference Proceedings
Consequence of violet laser irradiation on the optical properties of mawsoniteCu6Fe2SnS8 [CFTS] thin films deposited via semi-computerized spray pyrolysis technique
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Publication Date
Thu May 18 2023
Journal Name
Journal Of Engineering
The Effect of Tool Path Strategy on Mechanical Properties of Brass (65-35) in Single Point Incremental Sheet Metal Forming (SPIF)
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In this paper, three tool paths strategies; iso-planar, helical and adaptive have been implemented to investigates their effect on the mechanical properties of Brass 65-35 formed by single point incremental sheet metal forming process. To response this task, a fully digital integrated system from CAD modeling to finished part (CAD/CAM) for SPIF process has been developed in this paper.
The photo-micrographs shows an identical grain formation due to the plastic deformation of the incremental forming process, change in the grain shape and size was observed. It's found that the adaptive tool path play a significant role to increase the hardness of the formed specimen from (48 to 90 HV) and the grain texture of the formed specimen found a

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Publication Date
Wed Jun 01 2022
Journal Name
Iraqi Journal Of Physics
Effects of Hydrogen Peroxide Concentration on Properties of Black Silicon Fabricated by Two-Step Silver-Assisted Wet Chemical Etching for Photovoltaics
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Crystalline silicon (c-Si) has low optical absorption due to its high surface reflection of incident light. Nanotexturing of c-Si which produces black silicon (b-Si) offers a promising solution. In this work, effect of H2O2 concentrations towards surface morphological and optical properties of b-Si fabricated by two-step silver-assisted wet chemical etching (Ag-based two-step MACE) for potential photovoltaic (PV) applications is presented. The method involves a 30 s deposition of silver nanoparticles (Ag NPs) in an aqueous solution of AgNO3:HF (5:6) and an optimized etching in HF:H2O2:DI H2O solution under 0.62 M, 1.85 M, 2.47 M, and 3.7 M concentrations of H2O<

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Publication Date
Tue Aug 01 2017
Journal Name
Journal Of Multidisciplinary Engineering Science And Technology (jmest)
Study The Influence Of Sn Dopant On The Surface Topography And Some Physical Properties Of CdSe Films Prepared By Evaporation Technique
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Publication Date
Sun Nov 01 2020
Journal Name
Iop Conference Series: Materials Science And Engineering
Pump-Probe Technique to Study of the All-Optical Switching Properties of Copper Phthalocyanine Thin Film prepared via Pulsed laser deposition
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Abstract<p>Z-scan has been utilized for studying the non-linear properties and optical limiting behaviors of the dye Copper Phthalocyanine thin films. The refractive index is negative, which indicates a self-defocusing behavior and non-linear absorption coefficient (<italic>β</italic>) of CuPc is a positive sign is a result of RSA. The optical switching behaviors of dye have been researched with the use of the method of the pump-probe with 9ns Q-Switched Nd: YAG laser at pump beam equal to 532 nm and a probe beam equal to 630nm Diode laser. The thin films of copper Phthalocyanine also reflect a significant limiting of the optical power of CW laser with an adequate threshold of the opt</p> ... Show More
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Publication Date
Fri Jan 01 2021
Journal Name
Materials Today: Proceedings
Study the electronic and spectroscopic properties of ALxB7-XN7 Wurtzoids as a function of size and concentration using density functional theory
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Electronic properties including (bond length, energy gap, HOMO, LUMO and density of state) as well as spectroscopic properties such like infrared, Raman scattering, force constant, reduced mass and longitu- dinal optical mode as a function of frequency are based on size and concentration of the molecular and nanostructures of aluminum nitride ALN, boron nitride BN and AlxB7-XN7 as nanotubes has calculated using Ab –initio approximation method dependent on density functional theory and generalized gradient approximation. The geometrical structure are calculated by using Gauss view 05 as a complementary program. Shows the energy gap of ALN, BN and AlxB7-XN7 as a function of the total number of atoms , start from smallest molecule to reached

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