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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 May 25 2023
Journal Name
Polycyclic Aromatic Compounds
Effect of Modified Nano-Graphene Oxide and Silicon Carbide Nanoparticles on the Mechanical Properties and Durability of Artificial Stone Composites from Waste
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Sludge from stone-cutting (SSC) factories and stone mines cannot be used as decorative stones, stone powder, etc. These substances are left in the environment and cause environmental problems. This study aim is to produce artificial stone composite (ASC) using sludge from stone cutting factories, cement, unsaturated resin, water, silicon carbide nanoparticles (SiC-NPs), and nano-graphene oxide (NGO) as fillers. Nano graphene oxide has a hydrophobic plate structure that water is not absorbed due to the lack of surface tension on these plates. NGO has a significant effect on the properties of artificial stone due to its high specific surface area and low density in the composite. Its uniform distribution in ASC is very low due to its hydropho

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Publication Date
Fri May 01 2020
Journal Name
Journal Of Engineering
The Effects of Maximum Attapulgite Aggregate Size and Steel Fibers Content on Fresh and Some Mechanical Properties of Lightweight Self Compacting Concrete
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The main objectives of this study were investigating the effects of the maximum size of coarse Attapulgite aggregate and micro steel fiber content on fresh and some mechanical properties of steel fibers reinforced lightweight self-compacting concrete (SFLWSCC). Two series of mixes were used depending on maximum aggregate size (12.5 and 19) mm, for each series three different steel fibers content were used (0.5 %, 1%, and 1.5%). To evaluate the fresh properties, tests of slump flow, T500 mm, V funnel time, and J ring were carried out. Tests of compressive strength, splitting tensile strength, flexural tensile strength, and calculated equilibrium density were done to evaluate mechanical properties. For reference mixes, the

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Publication Date
Thu Feb 01 2024
Journal Name
Journal Of Materials Science: Materials In Electronics
Effect of graphene nanoplates and multi-walled carbon nanotubes doping on structural and optical properties of polyvinyl chloride membranes for outdoor applications
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Publication Date
Mon Jan 01 2018
Journal Name
Applied Science Reports
Facial Acne Therapy by Using Pumpkin Seed Oil with Its Physicochemical Properties
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The herbal remedy individually or in combination with standard medicines has been used in diverse medical treatises for the cure of different diseases. Pumpkin seed oil is one of the recognized edible oil and has substantial medicinal properties due to the presence of unique natural edible substances. Inflammation is an adaptive response that is triggered by noxious stimuli and conditions, which involves interactions amongst many cell types and mediators, and underlies many pathological processes. Unsaturated fatty acids (UFAs) can influence inflammation through a variety of mechanisms, and have been indicated as alternative anti-inflammatory agents to treat several inflammatory skin disorders. Pumpkin seed oil is rich in (UFAs), that its t

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Publication Date
Tue Aug 01 2017
Journal Name
Journal Of Molecular Structure
Asymmetric 1,3,4-thiadiazole derivatives: Synthesis, characterization and studying their liquid crystalline properties
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Publication Date
Sun Nov 17 2024
Journal Name
Journal Of Global Innovations In Agricultural Sciences
Mango Waste (Peel and Kernel) Enhances Food Dietary Fiber and Antioxidant Properties
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Biscuits are a global snack due to their convenience, variety, and durability. Biscuits with nutritious ingredients are in demand as customers become more health conscious. This change led to interest about utilizing agricultural by-products to enhance the nutritional value of widely consumed foods. Mango (Mangifera indica L.), a frequently cultivated tropical fruit, produces vital by-products during its processing, mainly comprising peels and kernels. The by-products, comprising around 35–60% of the mango fruit's weight, are high in bioactive compounds including dietary fiber, polyphenols, carotenoids, and essential fatty acids. Mango peels and kernels, even with their nutritional potential, frequently neglected, resulting in ris

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Publication Date
Sun Nov 17 2024
Journal Name
Journal Of Global Innovations In Agricultural Sciences
Mango Waste (Peel and Kernel) Enhances Food Dietary Fiber and Antioxidant Properties
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Biscuits are a global snack due to their convenience, variety, and durability. Biscuits with nutritious ingredients are in demand as customers become more health conscious. This change led to interest about utilizing agricultural by-products to enhance the nutritional value of widely consumed foods. Mango (Mangifera indica L.), a frequently cultivated tropical fruit, produces vital by-products during its processing, mainly comprising peels and kernels. The by-products, comprising around 35–60% of the mango fruit's weight, are high in bioactive compounds including dietary fiber, polyphenols, carotenoids, and essential fatty acids. Mango peels and kernels, even with their nutritional potential, frequently neglected, resulting in ris

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Publication Date
Sun Dec 02 2018
Journal Name
Iraqi Journal Of Physics
Optical properties for TiO2 / PMMA nanocomposite thin films prepared by plasma jet
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PMMA/TiO2 homogeneous thin films were deposited by using plasma jet system under normal atmospheric pressure and room temperature. PMMA/TiO2 nanocomposite thin film synthesized by plasma polymerization. Titanium oxide was mixed with Methyl Methacrylate Monomer (MMA) with specific weight ratios (1, 3 and 5 grams of TiO2 per 100 ml of MMA). Optical properties of PMMA/TiO2 nanocomposite thin films were characterized by UV-Visible absorption spectra using a double beam UV-Vis-NIR Spectrophotometer. The thin films surface morphological analysis is carried out by employing SEM. The structure analysis are achieved by X-ray diffraction. UV-Visible absorption spectra shows that the increasing the concentration of titanium oxide added to the polym

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Publication Date
Wed Mar 29 2023
Journal Name
Aip Conference Proceedings
(𝓹,𝔼)-convex sets and (𝓹,𝔼)-Convex functions with their properties
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Publication Date
Mon Mar 01 2021
Journal Name
Iraqi Journal Of Physics
Linear and Non-Linear Optical Properties for Organic Semiconductor (CuPc) Thin Films
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Thin films of CuPc of various thicknesses (150,300 and 450) nm have been deposited using pulsed laser deposition technique at room temperature. The study showed that the spectra of the optical absorption of the thin films of the CuPc  are two bands of absorption one in the visible region at about 635 nm, referred to as Q-band, and the second in ultra-violet region where B-band is located at 330 nm. CuPc thin films were found to have direct band gap with values around (1.81 and 3.14 (eV respectively. The vibrational studies were carried out using Fourier transform infrared spectroscopy (FT-IR). Finally, From open and closed aperture Z-scan data non-linear absorption coefficient and non-linear refractive index have been calculated res

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