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.
This research studies the effect of addition of some nanoparticles
(MgO, CuO) and grain size (30,40nm) on some physical properties
(impact strength, hardness and thermal conductivity) for a matrix
blend of epoxy resin with SBR rubber. Hand –Lay up method was
used to prepare the samples. All samples were immersed in water for
9 weeks.
The Results showed decreased in the values of impact strength and
hardness but increased the coefficient of thermal conductivity.
This study discussed the effects of doping with silver (Ag) on the optical and structural properties of
CdO nanoparticles at different concentrations 0, 1, 2, 3, 4, 5 wt% prepared by the precipitation method. The
materials were annealed at 550˚C for 1 h. The structural, topographical, and optical properties were
diagnosed by X-ray diffraction analysis, atomic force instrument, and visible and ultraviolet spectrometers.
The results show that the average diameter of the grains depends on the percentage of added silver to the
material, as the diameter decreased from 88.8 to 59.7 nm, and it was found that the roughness increased from
5.56 to 26.5. When studying the optical properties, it was noted that th
Resilient polymeric materials such as silicone elastomers are currently used for maxillofacial prostheses construction but the strength of these materials and their clinical performance need to be optimized with the addition of reinforcing fillers. This study investigates the effect of zirconia nanopowder addition on tear strength, tensile strength, elongation at break, Shore A hardness, surface roughness and cytotoxicity of VST-50 maxillofacial silicone. Silicone base was mixed with different amounts (1%, 2% and 3%) of zirconia nanopowder using a vacuum mixer. Silicone without filler was used as control for comparison. Scanning Electron Microscopy and Atomic Force Microscopy were utilized to assess the efficiency of high-shear vacuum mixin
... Show MoreSlurry-infiltrated fibrous concrete (SIFCON) is a special type of concrete that has great strength, as well as high ductility. However, the unit weight is high, which exceeds the unit weight of fiber-reinforced concrete, because of the high fiber content. This research aims to verify the compressive and flexural strength, as well as the density of SIFCON when using two different fibers (steel and polyolefin). Sometimes mono type of fiber steel or polyolefin, sometimes by hybridizing two types of fiber steel + polyplefin. Volume fraction (6% for all species) was used. Hook-end steel fiber and polyolefin fiber are used. With hybridization, a total volume fraction of 6% was used, which
A laboratory experiment was carried out and repeated at field of College of Agricultural Engineering Sciences, University of Baghdad in 2017. First factor was three cultivars of lupine 'Giza-1', 'Giza-2' and 'Hamburg'. Second factor was three seed weights (lower weight, medium weight and higher weight) which was following the cultivars factor. Nested design was used. Results showed supremacy of 'Giza-1' cultivar significantly and gave higher germination ratio, radical length, seedling dry weight, seedling vigour index, field emergence ratio, plant height and number of leaves per plant. The treatment ('Giza-1'×higher seed weight) was supremacy significantly and gave higher germination ratio, radical length, plumule length, and seedling vigo
... Show MoreCopper tin sulfide (Cu2SnS3) thin films have been grown on glass
substrate with different thicknesses (500, 750 and 1000) nm by flash
thermal evaporation method after prepare its alloy from their
elements with high purity. The as-deposited films were annealed at
473 K for 1h. Compositional analysis was done using Energy
dispersive spectroscopy (EDS). The microstructure of CTS powder
examined by SEM and found that the large crystal grains are shown
clearly in images. XRD investigation revealed that the alloy was
polycrystalline nature and has cubic structure with preferred
orientation along (111) plane, while as deposited films of different
thickness have amorphous structure and converted to polycrystalline
Some of the characters of the Staphylolysin A and D enzymes purified from Pseudomonas aeruginosa P16 and P5 respectively were studied, the molecular weights of Staphylolysin A and D were 20.417 kilo dalton and 23.988 kilo Dalton respectively by SDS- polyacryl amide gel electrophoresis. The optimum pH for staphylolysin A activity was found to be 8 which gives higher activity reaches 150 unit/ml, and for enzyme stability was 7.5-8.5 in which the enzyme nearly retained its full activity, while it was 9.5 for staphylolysin D that gives higher activity of 16 unit/ml,and 8.5-9.5 for enzyme stability in which the enzyme nearly retained its full activity, Maximum activity of two enzymes was obtained at 40C in which the specific activity for st
... Show MoreThe electronic properties and Hall effect of thin amorphous Si1-xGex:H films of thickness (350 nm) have been studied such as dc conductivity, activation energy, Hall coefficient under magnetic field (0.257 Tesla) for measuring carrier density of electrons and holes and Hall mobility as a function of germanium content (x = 0–1), deposition temperature (303-503) K and dopant concentration for Al and As in the range (0-3.5)%. The composition of the alloys and films were determined by using energy dispersive spectroscopy (EDS) and X-ray photoelectron spectroscopy (XPS).
This study showed that dc conductivity of a-Si1-xGex:H thin films is found to increase with increasing Ge content and dopant concentration, whereas conductivity activati
In this research study the effect of fish in alternating electrical properties at room temperature copper oxide membranes and fish prepared in a manner different thermal spraying chemical on a thin glass bases and heated