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 primary purpose of this paper is to introduce the, N-coprobabilistic normed space, coprobabilistic dual space of N-coprobabilistic normed space and give some facts that are related of them.
In this work, we study the effect of doping Sn on the structural and optical properties of pure cadmium oxide films at different concentrations of Tin (Sn) (X=0.1,0.3 and 0.5) .The films prepared by using the laser-induced plasma at wavelength of laser 1064 nm and duration 9 ns under pressure reached to 2.5×10-2 mbar. The results of X-ray diffraction tests showed that the all prepared films are polycrystalline. As for the topography of the films surface, it was measured using AFM , where the results showed that the grain size increases with an increase in the percentage of doping in addition to an increase in the average roughness. The optical properties of all films have also been studied through the absorbance s
... Show MoreA thin CdS Films have been evaporated by thermal evaporation technique with different thicknesses (500, 1000, 1500 and 2000Å) and different duration times of annealing (60, 120 180 minutes) under 573 K annealing temperature, the vacuum was about 8 × 10-5 mbar and substrate temperature was 423 K. The structural properties of the films have been studied by X- ray diffraction technique (XRD). The crystal growth became stronger and more oriented as the film thickness (T) and duration time of annealing ( Ta) increases.
Abstract Background: The daily usage of maxillofacial prostheses causes them to mechanically deteriorate with time. This study was aimed to evaluate the reinforcement of VST50F maxillofacial silicone by using yttrium oxide (Y2O3) nanoparticles (NPs) to resist aging and mechanical deterioration. Materials and Method: Y2O3 NPs (30–45nm) were loaded into VST50F maxillofacial silicone in two weight percentages (1 and 1.5 wt%), which were predetermined in a pilot study as the best rates for improving tear strength with minimum increase in hardness values. A total of 120 specimens were prepared and divided into the control and experimental groups (with 1 and 1.5 wt% Y2O3 addition). Each group included 40 specimens, 10 specimens for each paramet
... Show MoreThe object of research is studying Raman scattering technique, photoluminescence and some optical properties of silver nanoparticles created by eco-friendly technique which independent on a long time, effort, energy and high temperatures, and with the highest adsorption capacity in order to achieve a high inhibition to paralyze the activity of the bacterial wall, by achieving the highest surface plasmon resonance (SRR). Silver nanoparticles were prepared using Matricaria Flower extract. Characterization of silver nanoparticles and detection of their effectiveness against microbial using two types of bacteria (Escherichia Coli and Staphylococcus aureus ), these nanoparticles were measured using a number of measurements, X-ray diffrac
... Show MoreMany designs have been suggested for unipolar magnetic lenses based on changing the width of the inner bore and fixing the other geometrical parameters of the lens to improve the performance of unipolar magnetic lenses. The investigation of a study of each design included the calculation of its axial magnetic field the magnetization of the lens in addition to the magnetic flux density using the Finite Element Method (FEM) the Magnetic Electron Lenses Operation (MELOP) program version 1 at three different values of current density (6,4,2 A/mm2). As a result, the clearest values and behaviors were obtained at current density (2 A/mm2). it was found that the best magnetizing properties, the high
... Show MoreNumber of new polyester and polyamide are prepared as derivatives from 5,5`-(1,4-phenylene)-bis-(1,3,4-thiadiazole-2-amine) [C1], three series of heterocyclic compounds were synthesized.The first series includes the Schiff base [C2] prepared from the reaction between compound [C1] with p-hydroxy benzaldehyde in presence of acetic acid and absolute ethanol , then these derivatives have reaction with maleic anhydride , phthalic anhydride and sodium azide, respectively to obtain the compounds [C3-5] contaning (oxazepine and tetrazole) rings.The third series of compounds [C1-5] has transformed to their polymers [C6-15] by reaction with adipoyl chloride and glutroyl chloride , respectively. The reaction was followed by T.L.C and ident
... Show MoreThe study was carried out in plant tissue culture laboratory, University of Baghdad during the period 2017-2019, as factorial experiment in complete randomized design, to study the effect of PEG at (0, 2, 4, 6 and 8%) on physiological and chemical changes in callus of three sunflower (Ishaqi 1, Aqmar and Al-haga) induced by the cultivation of the young stem in vitro under water stress. The content of callus cells of SOD, POD, CAT and APX enzymes as well as total dissolved carbohydrate were determined as indicators to determine the effect of PEG in callus tissue cells cultivated on medium equipped with the PEG concentrations. The results showed that cultivars were differs significantly, and A-haja variety was superior in increasing SOD to 12
... Show MoreBackground: Fluoridated acrylic resin material can present more stable properties when compared with conventional one.The most widely used fluoride –containing substance added to dental resin materials is sodium fluoride (Naf). This study evaluated the effect of Naf in different concentration to the acrylic resin denture base material and its effect on tensile strength ,modules of elasticity with long –term water immersion (after 4 months immersion in de-ionized water) Materials and methods: Eighty specimens from dumbbells shaped metal pattern for tensile strength test were preparedaccording to ISO 527: 1993 plastic –Determination tensile properties ,in dimensions(60mm, 12mm, 3 ± 0.2mm) length, width and depth respec
... Show MoreEnhancing asphalt binder performance against anticipated distresses is a critical focus in pavement engineering. This study investigates the synergistic influence of nano titanium dioxide (NT) and nano zinc oxide (NZ) on asphalt binder performance. Nine NT:NZ combinations (1:1 to 3:3) were prepared with 1–3% by binder weight, in addition to a reference binder (RB). The performance test program included; conventional tests (penetration, softening point, viscosity, and ductility), Dynamic Shear Rheometer (DSR) for performance grading, Multiple Stress Creep Recovery (MSCR) for rutting evaluation, and Linear Amplitude Sweep (LAS) for fatigue resistance. Furthermore, Statistical analysis (ANOVA) was performed to determine the significa
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