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.
The present work shows a theoretical results that have been used the functional Hybrid of three parameters Lee-Yang-Parr (B3LYP) of the quantum mechanical approach for density functional theory with (Spanish Initiative for Electronic Simulations with Thousands of Atoms) SIESTA code. All calculations were carried out employing the used method at the Gaussian 09 package of programs. It was reported the main point for research on dominance of the bandgap of elongated pi-conjugated molecules by using different chemical groups replacing hydrogen atom in the most molecules that used in this work. The side groups creates another factor that controls the value of the band gap. The dihedral angle between the two pheny
... Show MoreZnIn2(Se1-xTex)4 (ZIST) chalcopyrite semiconductor thin films at various contents (x = 0.0, 0.2, and 0.4) are deposited on glass and p type silicon (111) substrate to produce heterojunction solar cell by using the thermal evaporation technique at RT where the thickness of 500 nm with a vacuum of 1×10-5 mbar and a deposited rates of 5.1 nm/s. This study focuses on how differing x content effect on the factors affecting the solar cell characteristics of ZIST thin film and n-ZIST/p-Si heterojunction. X-ray diffraction XRD investigation shows that this structure of ZIST film is polycrystalline and tetragonal, with (112) preferred orientation at 2θ ≈ 27.01. Moreover, atomic force microscopy AFM is studying the external morphology of
... Show MoreCuInSe2 (CIS)thin films have been prepared by use vacuum thermal evaporation technique, of 750 nm thickness, with rate of deposition 1.8±0.1 nm/sec on glass substrate at room temperature and pressure (10-5) mbar. Heat treatment has been carried out in the range (400-600) K for all samples. The optical properties of the CIS thin films are been studied such as (absorption coefficient, refractive index, extinction coefficient, real and imaginary dielectric constant)by determined using Measurement absorption and transmission spectra. Results showed that through the optical constants we can made to control it is wide applications as an optoelectronic devices and photovoltaic applications.
Conventional flexible pavements are released to different types of failure in the initial phases of their service life due to high traffic density, high speeds, heavy loads, and harsh climates. To eliminate pavement damage and failure early, the present search investigates the impact of adding glass, steel, and basalt fibers in the asphalt mixtures. Also, the study evaluates these materials characteristics compared to the mixtures without fibers. The Marshall test and tensile strength ratio test (TSR) were utilized to evaluate the asphalt mixture's performance. A set of specimens were produced by incorporating glass fiber (GF), steel fiber (SF), and basalt fiber (BF) at (0.10%, 0.15%, 0.20%), (0.25%, 0.35%, 0.45%), and (0.15%, 0.35%
... Show MoreBackground: Deterioration of maxillofacial silicone properties due to microbial colonization is a common problem and leads to the replacement of the prosthesis. Incorporation of the antimicrobial agent into the silicone could be a solution. The purpose of this study was to evaluate the effect of silver-zinc zeolite addition on some mechanical properties of a maxillofacial silicone (VST-50). Materials and methods: Total 120 specimens were fabricated and divided into 3 groups: 40 specimens for tear strength test, 40 specimens for tensile and percentage of elongation tests and 40 specimens for Shore A hardness and surface roughness. Each group was divided into 4 subgroups according to the amount of zeolite added (0% “control”, 0.5%, 1% and
... Show MorePorous Silicon (PSi) has been produced in this work by using Photochemical (PC) etching process by using a hydrofluoric acid (HF) solution. The irradiation has been achieved using quartz- tungsten halogen lamp. The influence of various irradiation times on the properties of PSi اmaterial such as layer thickness, etching rate and porosity was investigated in this work too.
The XRD has been studied to determine the crystal structure and the crystalline size of PSi material
Study of the Mechanical and Electrical Properties of Modified Unsaturated Polyester Blends