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.
In this work, zinc oxide nanoparticles (ZnONPs) and sawdust/epoxy composite (20:80) were mixed using a simple molding method with different ZnONPs concentrations of (0.1, 0.3, 0.5, 0.7, and 1.0 %). The samples of the nanocomposites were characterized by the Scanning Electron Microscopy (SEM) technique to demonstrate the homogeneity of the prepared ZnONPs/nanocomposites. The photocatalytic activity of the samples was examined using the methylene blue (MB) dye as a pollutant solution, through evaluation of the efficiency of the prepared compound in the treatment of organic pollutants under illumination by sunlight. The photocatalytic results showed that after 240 minutes of exposure to sunlight, the sample prepared using (0.5 vol.% of ZnON
... Show MorePlastic soil exhibits unfavorited geotechnical properties (when saturation), which causes negative defects to engineering structures. Different attempts (included various materials) were conducted to proffer solutions to such defects by experimenting in practical ways. On one hand, these attempts aimed to improve the engineering characteristics of plastic soil, and on the other hand, to use problematic waste materials as a stabilizer, like cement kiln dust, and to reduce environmental hazards. This paper explored the shrinkage, plasticity, and strength behavior of plastic soil enhanced with cement dust. The cement dust contents were 0%, 5%, 10%, 15% and 20% by dry weight of soil. An experimental series of shrinkage and p
... Show More57 isolates of Mycobacterium tuberculosis and Mycobacterium bovis were identified; they were isolated from different clinical sources which included sputum, bronchial wash, abscess, pleural fluid, gastric fluid, eye fluid, and CSF, also urine and ear swab. This investigation was carried out on 198 patient attended National Reference Laboratory for T.B during September 2009. Also the study declared that the ratio of separation of this bacterium from male was (67.6%) and it’s higher than the ratio of separation this bacterium from females which was (32.3%). The susceptibility of Mycobacterium tuberculosis to melatonin was evaluated. Many concentrati
... Show MoreIn this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on is also introduced with the prove that a fuzzy seminorm on
... Show MoreIn this study we examine variations in the structure of perovskite compounds of LaBa2Cu2O9, LaBa2CaCu3O12 and LaBa2Ca2Cu5O15 synthesized using the solid state reaction method. The samples’ compositions were assessed using X-ray fluorescence (XRF) analysis. The La: Ba: Ca: Cu ratios for samples LaBa2Cu2O9, LaBa2CaCu3O12 and LaBa2Ca2Cu5O15 were found by XRF analysis to be around 1:2:0:2, 1:2:1:3, and 1:2:2:5, respectively. The samples’ well-known structures were then analyzed using X-ray diffraction. The three samples largely consist of phases 1202, 1213, and 1225, with a trace quantity of an unknown secondary phase, based on the intensities and locations of the diffraction peaks. According to the measured parameters a, b, and c, every sa
... Show MoreThe study effect Graphene on optical and electrical properties of glass prepared on glass substrates using sol–gel dip-coating technique. The deposited film of about (60-100±5%) nm thick. Optical and electrical properties of the films were studied under different preparation conditions, such as graphene concentration of 2, 4, 6 and 8 wt%. The results show that the optical band gap for glass-graphene films decreasing after adding the graphene. Calculated optical constants, such as transmittance, extinction coefficient are changing after adding graphene. The structural morphology and composition of elements for the samples have been demonstrated using SEM and EDX. The electrical properties of films include DC electrical conductivity; we
... Show MoreTitanium alloy surface properties have an essential role in the interaction of dental implants with bone, and alteration of the surface of the implant could improve osseointegration. This study was designed to investigate the effect of different heat treatment temperatures on titanium alloy surface properties for dental implants. The effect of different temperatures of heat treatment (750°C, 850°C, 950°C and 1050°C) were investigated on the surface topography, surface chemistry, titanium oxide layer thickness, blood contact angle, & blood drop diameter of titanium alloy. The disks were prepared from titanium alloy (Ti-6Al-4V) and the samples were divided into five groups depending on the different temperatures of heat treatment. The hea
... Show MoreBentonite is widely used in industrial applications. The present study reports the effect of adding different weights of ZnO to the Iraqi bentonite, on surface area, pore volume and real density. These surface properties were evaluated for pure and modified bentonite. The modification was made by adding different ZnO weights such as; ( 0.5%, 1%, 5%, 10% ). The effect of heat exposing for all modified clay samples at 500 ?C have been also evaluated. The results show that the addition of 0.5% ZnO leads to increase the surface area percentage about 36%, increase pore volume percentage about 5.48% and increase the real density percentage about 27.116%. When the samples exposed to 500 ?C, their surface area and pore volumes have been decreased a
... Show MoreIn this paper the definition of fuzzy anti-normed linear spaces and its basic properties are used to prove some properties of a finite dimensional fuzzy anti-normed linear space.