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.
Eruca sativa (jarjeer) is an annual herb (family Brassicaceae), which contains a wide range of chemicals and minerals with nutraceutical and organoleptic characteristics. Jarjeer was generally used as a food and traditionally mainly consumed due to its aphrodisiac properties. This crop known to contain various phytochemicals such as flavonoids, phenolic acids, terpens, carotenoids, tannins, glycosides, saponins, sterols, alkaloids, and other secondary metabolites. In leaves, kaempferol and its derivatives, glucosativin, are the main flavonoids and glucosinolate, respectively, while erucic acid and glucoerucin are the main fatty acid and glucosinolate, respectively. Medicinally, the plant has antibacterial, antidiabetic, antihyperten
... Show MoreBackground: The incorporation of rubber has not been entirely successful because it can have detrimental effects on the transverse Strength and hence the rigidity of the denture base. Materials and methods: Zirconium oxide nanoparticales were coated with a layer of trimethoxysilylpropylmethacrylate (TMSPM) before sonication in monomer (MMA) with the percentages 3% by weight then mixed with powder using conventional procedure.(100) samples were prepared and divided into five groups according to the test performed ,Each group consisted of 20 specimens and these were subdivided into 2 groupsGroup (A): control group (10 specimens of high impact acrylic resin without zirconium oxide) and Group (B):zirconium oxide group(10 specimens of high impac
... Show MoreIn this paper, silicon carbonitried thin films were prepared by the method of photolysis of the silane (SiH4) and ethylene (C2H4) gases, with and without ammonia gas (NH3), which is represented by the ratio between the (PNH3) and (PSiH4 + PC2H4 + PNH3), (which assign by the letter X), X has the values (0, 0.13, 0.33). This method carried out by using TEA-CO2 laser, on glass substrate at (375 oC), deposition rate (0.416-0.833) nm/pulse thin film thickness of (500-1000) nm. The optical properties of the films were studied by using Absorbance and Transmittance spectrums in wavelength range of (400-1100) nm, the results showed that the electronic transitions is indirect and the energy gap for the SiCN films increase with increasing of nitrog
... Show MoreSelf-compacted concrete (SCC) considered as a revolution progress in concrete technology due to its ability for flowing through forms, fusion with reinforcement, compact itself by its weight without using vibrators and economic advantages. This research aims to assess the fresh properties of SCC and study their effect on its compressive strength using different grading zones and different fineness modulus (F.M) of fine aggregate. The fineness modulus used in this study was (2.73, 2.82,2.9& 3.12) for different zones of grading (zone I, zone II& marginal zone(between zone I&II)) according to Iraqi standards (I.Q.S No.45/1984).Twelve mixes were prepared, each mix were tested in fresh state with slump, V-Funnel and L-Box tests, then 72
... Show MoreSelf-compacted concrete (SCC) considered as a revolution progress in concrete technology due to its ability for flowing through forms, fusion with reinforcement, compact itself by its weight without using vibrators and economic advantages. This research aims to assess the fresh properties of SCC and study their effect on its compressive strength using different grading zones and different fineness modulus (F.M) of fine aggregate. The fineness modulus used in this study was (2.73, 2.82,2.9& 3.12) for different zones of grading (zone I, zone II& marginal zone(between zone I&II)) according to Iraqi standards (I.Q.S No.45/1984).Twelve mixes were prepared, each mix were tested in fresh state with slump, V-Funnel and L-Box tests, t
... Show MoreRandom laser gain media is synthesized with different types of dye at the same concentration (1×10-3 M) as an active material and silicon dioxide NPs (silica SiO2) as scatter centers through the Sol-Gel technique. The prepared samples are tested with UV–Vis spectroscopy, Fluorescence Spectroscopy, Field Emission Scanning Electron Microscopy (FESEM), and Energy Dispersive X-ray Diffraction (EDX). The end result demonstrates that doped dyes with silica nanoparticles at a concentration of 0.0016 mol/ml have lower absorbance and higher fluorescence spectra than pure dyes. FESEM scans revealed that the morphology of nanocrystalline silica is clusters of nano-sized spherical particles in the range (25-67) nm. It is con
... Show MoreBackground: Poly propylene fibers with and without silane treatment have been used to reinforce heat cure denture base acrylic but, some mechanical properties like transverse strength, impact strength, tensile strength, hardness, wear resistance and wettability. Which are related to the clinical use of the prosthesis are not evaluated yet. The aim of the study is to identify the influence of incorporation of treated and untreated fibers on these properties Materials and methods: Eighty four heat cure acrylic specimens were constructed by conventional flasking technique. They were divided into six groups according to the tests and each group was subdivided into two subgroups control and experimental groups (seven samples for each subgroup
... Show MoreIn this work Study effect of annealing temperature on the Structure
of a-Se and electrical properties of a-Se/c-Si hetrojunction have been
studied.The hetrojunction fabricated by deposition of a-Se film on c-
Si using thermal evaporation.
Electrical properties of a-Se/ c-Si heterojunction include I-V
characteristics, in dark at different annealing temperature and C-V
characteristics are considered in the present work.
C-V characteristics suggested that the fabricated diode was
abrupt type, built in potential determined by extrapolation from
1/C2-V curve. The built - in potential (Vbi) for the Se/ Si System
was found to be increase from 1.21 to 1.62eV with increasing of
annealing temperature
Oil pollution of the soil due to a leakage in oil tubes, transportation of products, or during oil excavations can change the soil physical and mechanical, chemical, and biological properties. Consequently, the soil may or may not be eligible for engineering construction projects and it may need a significant treatment. Therefore, it is required to have a better understanding of the general behavior and the corresponding geotechnical properties upon pollution particularly for those areas associated with oil explorations and industry like Thi-Qar Governorate. Fine and coarse soils from two sites at the University of Thi-Qar are artificially contaminated with oil products ranging from 0% to 10% of their dry weight. Testing programs have been
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