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.
Reservoir characterization is an important component of hydrocarbon exploration and production, which requires the integration of different disciplines for accurate subsurface modeling. This comprehensive research paper delves into the complex interplay of rock materials, rock formation techniques, and geological modeling techniques for improving reservoir quality. The research plays an important role dominated by petrophysical factors such as porosity, shale volume, water content, and permeability—as important indicators of reservoir properties, fluid behavior, and hydrocarbon potential. It examines various rock cataloging techniques, focusing on rock aggregation techniques and self-organizing maps (SOMs) to identify specific and
... Show MoreIntroduction/Aim. Seminal fluid analysis (SFA) plays a crucial role in helping infertility clinics diagnose the underlying reason of male infertility. The aim of the study was to investigate seminal fluid patterns of male partners of an infertile couple with apparently fertile female partners. Materials and methods. A cross-sectional study was conducted between January 2019 and December 2022. Patients were attending consultations for delayed conception for more than 12 months with apparently fertile female partner. Results. Four hundred fifty-three patients were included in the study. The distribution of patients according to age groups showed that 277 patients were young, aged 21 - 30 years (61%). Two hundred sixty-two (58%) patien
... Show MoreThe dynamic thermomechanical properties, sealing ability, and voids formation of an experimental obturation hydroxyapatite-reinforced polyethylene (HA/PE) composite/carrier system were investigated and compared with those of a commercial system [GuttaCore (GC)]. The HA/PE system was specifically designed using a melt-extrusion process. The viscoelastic properties of HA/PE were determined using a dynamic thermomechanical analyser. Human single-rooted teeth were endodontically instrumented and obturated using HA/PE or GC systems, and then sealing ability was assessed using a fluid filtration system. In addition, micro-computed tomography (μCT) was used to quantify apparent voids within the root-canal space. The data were statistically analys
... Show MoreThis study was conducted to determine the ability of water treatment system (Vortisand) to reduce some chemical and physical properties for tigris river raw water, It consisted of turbidity, electrical conductivity, pH, total hardness, calcium Hardness as well as temperature in order to determine the unit`s efficiency for reducing their concentration as compared to those in the water produced by some classical potable water projects (Dora and Wathba) in Baghdad. Samples were collected during the cold months (December 2016 and January 2017) and during the hot months (May and June 2017). The results showed that this system has the ability to reduce some properties such as turbidity, the values were 215NTU in raw water and decreased to NTU
... Show MoreSteps were taken to obtain the Kojic acid crystals from local fungal isolation A. flavus WJF81 by separating the fermentation products from the fungus mycelium from the production plant at the centrifuge at a speed of 5000 cycles for 10 minutes. The extraction was followed by ethyl acetate then supernatant concentrate by using rotary evaporator, and dried with heat oven 37ºC. Long, yellowish, pristine acid crystals were obtained that examined the optical microscope with a magnification force of 10x and 40x. The melting point of kojic acid was determined between 152.9-153.5 °C Results of the diagnosis of Kojic acid by applying High pressure liquid chromatography HPLC technique showed that the acid was at one peak, which was close to the
... Show MoreIn this work, the effects of size, and temperature on the linear and nonlinear optical properties in InGaN/GaN inverse parabolic and triangular quantum wells (IPQW and ITQW) for different concentrations at the well center were theoretically investigated. The indium concentrations at the barriers were fixed to be always xmax = 0.2. The energy levels and their associated wave functions are computed within the effective mass approximation. The expressions of optical properties are obtained analytically by using the compact density-matrix approach. The linear, nonlinear, and total absorption coefficients depending on the In concentrations at the well center are investigated as a function of the incident photon energy for different
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