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.
At the temperature 298.15 K, some physical properties such as: refractive indices (nD), viscosities (η) and densities (ρ) were studied in four liquid-liquid mixtures: carboxylic acids (HCOOH, CH3COOH, CH3CH2COOH and CH3CH2CH2COOH) with tetrahydrofurfuryl alcohol (THFA) with the identified configuration set. These empirical data were utilized to estimate the excess molar volumes (Vm E), refractive index perversions (ΔR), viscosity deviations (ηE) and excess molar Gibbs free energy (ΔG*E). Values of Vm E, ηE , ΔG*E and ΔR were plotted versus mole fraction of tetrahydrofurfuryl alcohol. In all cases, the values of Vm E, ηE , ΔG*E and ΔR that obtained in this study were found to be negative at 298.15 K. The excess parameters
... Show MoreIn this work, varying compositions of SiO2 micro filler were added
with the Polyvinyl Chloride (PVC) and samples have been prepared
using film casting technique. The results have been analyzed and
compared for PVC samples with (1 wt%, 3 wt%, 5 wt% and 10 wt%)
SiO2 micro filler. Mechanical characteristics such as tensile strength,
elongation at break and Young`s modulus were measured for all the
samples, where the tensile strength was increased from 8.39 Mpa for
purified PVC to 16 Mpa for 3% SiO2/PVC composite. Also, thermal
conductivity measurement values illustrated that composite materials
have a good thermal insulation at 10 wt. %, thermal conductivity was
decreased from 0.1684 W/m.
Background: The geriatric patients wearing removable partial dentures are increasing in proportion. At the same time, the root caries prevalence accompanied by gingival recession is increasing. A variety of vehicles can deliver fluoride into the oral cavity, including fluoride mouth-rinse, fluoride dentifrice, topical fluoride, and fluoride-releasing restorative materials, all of which effectively prevent root caries and suppress recurrent caries. This study aimed to evaluate the effect of sodium fluoride addition on some mechanical properties of heat cure acrylic denture base material. Material and method: A total of 90 samples were prepared in this study, then divided into three main groups according to the type of test used (hardness, te
... Show MoreThe accumulation of construction and demolition waste is one of the major problems in modern construction. Hence, this research investigates the use of waste brick in concrete. Seven different concrete mixes were investigated in this study: a control concrete mix, three mixes with volumetric replacement (10, 20, and 30)% of natural aggregate with brick aggregate, and two mixes with the addition of nano brick powder at a percentage level of 5– 10% by weight of cementitious materials. And the last one was mixed with 10% nano brick and 10% coarse brick aggregate. The experimental results for the additive of nano brick powder showed an enhancement in mechanical properties (compressive,
In This paper, CuO thin films having different thickness (250, 300 , 350 and 400) nm were deposited on glass substrates by thermal vacuum evaporator. The thermal oxidation of this evaporated film was done in heated glass at temperature (300 in air at one hour. The study of X-ray diffraction investigated all the exhibit polycrystalline nature with monoclinic crystal structure include uniformly grains. Thin film’s internal structure topographical and optical properties. Furthermore, the crystallization directions of CuO (35.54 , 38.70 ) can be clearly observed through an X-ray diffraction analysis XRD, Atomic Force Microscope AFM (topographic image) showed that the surface Characteristics , thin films crystals grew with increases in either
... Show MoreIn this study, an improved process was proposed for the synthesis of structure-controlled Cu2O nanoparticles, using a simplified wet chemical method at room temperature. A chemical solution route was established to synthesize Cu2O crystals with various sizes and morphologies. The structure, morphology, and optical properties of Cu2O nanoparticles were analyzed by X-ray diffraction, SEM (scanning electron microscope), and UV-Vis spectroscopy. By adjusting the aqueous mixture solutions of NaOH and NH2OH•HCl, the synthesis of Cu2O crystals with different morphology and size could be realized. Strangely, it was found that the change in the ratio of de-ionized water and NaOH aqueous solution led to the synthesis of Cu2O crystals of differen
... Show MoreIn the present work, the ternary compound MgxZn7-x O7Wurtzoid with variable Zn and Mg contents was analyzed using density functional theory with B3LYP 6-311G**basis set. The electronic and vibrational properties of MgxZn7-xO7 wurtzoids, were investigated, including energy gaps, bond lengths, spectral properties, such like infrared spectra and Raman. IR and Raman spectra were compared with experimental longitudinal optical modes frequency results. The theoretical results agree well with experiments and previous data. It has been found that the energy gap is increasing with the increased Mg concentration, and that the longitudinal optical position exposes a UV shift movement with an increase in the concentration.
According to the theory of regular geometric functions, the relevance of geometry to analysis is a critical feature. One of the significant tools to study operators is to utilize the convolution product. The dynamic techniques of convolution have attracted numerous complex analyses in current research. In this effort, an attempt is made by utilizing the said techniques to study a new linear complex operator connecting an incomplete beta function and a Hurwitz–Lerch zeta function of certain meromorphic functions. Furthermore, we employ a method based on the first-order differential subordination to derive new and better differential complex inequalities, namely differential subordinations.
This article studied some linear and nonlinear optical characteristics of different pH solutions from anthocyanin dye extract at 180 oC from red cabbage. First, the linear spectral characteristics, including absorption and transmittance in the range 400-800 nm for anthocyanin solution 5% v/v with different pHs, were achieved utilizing a UV/VIS spectrophotometer. The experimental results reveal a shift in the absorption toward the longer wavelength direction as pH values increment. Then, the nonlinear features were measured using the Z-scan technique with a CW 532 nm laser to measure the nonlinear absorption coefficient through an open aperture. A close aperture (diameter 2 mm) calculates the nonlinear refractive index. The open Z-scan sh
... Show MoreIn this paper, chip and powder copper are used as reinforcing phase in polyester matrix to form composites. Mechanical properties such as flexural strength and impact test of polymer reinforcement copper (powder and chip) were done, the maximum flexural strength for the polymer reinforcement with copper (powder and chip) are (85.13 Mpa) and (50.08 Mpa) respectively was obtained, while the maximum observation energy of the impact test for the polymer reinforcement with copper (powder and chip) are (0.85 J) and (0.4 J) respectively