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.
Background: Orthodontic mini-implants are increasingly used in orthodontics and the bone density is a very important factor in stabilization and success of mini-implant. The aim of this study was to observe the relationship among maximum bite force (MBF); body mass index (BMI); face width, height and type; and bone density in an attempt to predict bone density from these variables to eliminate the need for CT scan which have a highly hazard on patient. Materials and Methods: Computed tomographic (CT) images were obtained for 70 patients (24 males and 46 females) with age range 18-30 years. The maxillary and mandibular buccal cortical and cancellous bone densities were measured between 2nd premolar and 1st molar at two levels from the alveol
... Show MoreAn optical system including quantum dot cylindrical Fresnel lens (CFL) has been designed by using Zemax optical designing program. Quantum dot cylindrical Fresnel lens has a relatively small thickness compared to conventional lenses and high absorbance. It contains grooves in the form of parallel lines, and each groove represents an individual lens that works to change the path of light falling on it to a single focal line. (CFL) is characterized by its small focal length despite its large area and small thickness, due to the nature of its design that gives this feature, which is applied in many optical systems (imaging and non- imaging system). In this paper, the visual properties of the (CFL) were studied as it is one of the impor
... Show MoreOne of the major problems in modern construction is the accumulation of construction and demolition waste; this study thus examines the consumption of waste brick in concrete based on the use of blended nano brick powder as replacement for cement and as a fine aggregate. Seven concrete mixes were developed according to ACI 211.1 using recycled waste brick. Nano powder brick at 0, 5, and 10% was used as a replacement by cement weight, with other mixes featuring 10, 20, and 30% partial replacement by volume of river sand with brick. The experimental results for replacement of cement with nano brick powder showed an enhancement in mechanical properties (compressive, flexural, and tensile strength) at 7,
This paper displays a survey about the laboratory routine core analysis study on ten sandstone core samples taken from Zubair Reservoir/West Quarna Oil Field. The Petrophysical properties of rock as porosity, permeability, grain's size, roundness and sorting, type of mineral and volumes of shales inside the samples were tested by many apparatus in the Petroleum Technology Department/ University of Technology such as OFITE BLP-530 Gas Porosimeter, PERG-200TM Gas Permeameter and liquid Permeameter, GeoSpec2 apparatus (NMR method), Scanning Electron Microscopy (SEM) and OFITE Spectral Gamma Ray Logger apparatus. By comparing all the results of porosity and permeability measured by these instruments, it is clear a significant vari
... Show MoreThe research aims to investigate the effects of GMAW or MIG welding process on the mechanical properties of dissimilar aluminum alloys 2024-T351 and AA 6061- T651. A series of experimental techniques have been conducted to evaluate mechanical properties of the alloys, by carrying out hardness, tensile and bending tests for welded and un-welded specimens.
Metal inert gas (MIG) has been carried out on sheet metal using ER- 4043(AlSi5) as a filler metal and argon as shielded gas. The welded joints were tested by X-ray radiography and Faulty pieces were excluded.
Welding joints without defects are subjected to heat treatment including heating the joints in furnace to 170 °C for half an hour then air cooling to rel
... Show MoreA polycrystalline CdSe thin films doped with (5wt%) of Cu was fabricated using vacuum evaporation technique in the substrate temperature range(Ts=RT-250)oC on glass substrates of the thickness(0.8?m). The structure of these films are determined by X-ray diffraction (XRD). The X-ray diffraction studies shows that the structure is polycrystalline with hexagonal structure, and there are strong peaks at the direction (200) at (Ts=RT-150) oC, while at higher substrate temperature(Ts=150-250) oC the structure is single crystal. The optical properties as a function of Ts were studied. The absorption, transmission, and reflection has been studied, The optical energy gap (Eg)increases with increase of substrate temperature from (1.65
... Show MoreIn this paper, a study was made to determine the properties of Jovian radio bursts emitted at frequency 20.1MHZ. The data were provided from the Radio Jove archive for twelve years (2000-2012) for multi stations. The duration time for Long bursts (L) was (10-30) seconds and for Short bursts (S) was (10-20) seconds. The effect of radio bursts from the Sun and the galactic background were calculated at the same frequency and were found that radio bursts from the Sun will reduce the occurrence probability of Jovian radio bursts much more than radio bursts from the galactic background. The distribution of Jovian radio bursts was different; the occurrence probability with respect to the northern latitudes was more than the southern latitudes.
Zinc Oxide (ZnO) is probably the most typical II-VI
semiconductor, which exhibits a wide range of nanostructures. In
this paper, polycrystalline ZnO thin films were prepared by chemical
spray pyrolysis technique, the films were deposited onto glass
substrate at 400 °C by using aqueous zinc chloride as a spray
solution of molar concentration of 0.1 M/L.
The crystallographic structure of the prepared film was analyzed
using X-ray diffraction; the result shows that the film was
polycrystalline, the grain size which was calculated at (002) was
27.9 nm. The Hall measurement of the film studied from the
electrical measurements show that the film was n-type. The optical
properties of the film were studied using
The aim of this research is to study the surface alteration characteristics and surface morphology of the superhydrophobic/hydrophobic nanocomposite coatings prepared by an electrospinning method to coat various materials such as glass and metal. This is considered as a low cost method of fabrication for polymer solutions of Polystyrene (PS), Polymethylmethacrylate (PMMA) and Silicone Rubber (RTV). Si were prepared in various wt% of composition for each solutions. Contact angle measurement, surface tension, viscosity, roughness tests were calculated for all specimens. SEM showed the morphology of the surfaces after coated. PS and PMMA showed superhydrophobic properties for metal substrate, while Si showed hydroph
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