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.
It aim current researchs֬ to identify the impact of a proposed strategy in accordance with the objectives of science in the achievement and some science processes, where the experimental method was adopted, and define the research community was students second grade averag in Education Bagdad / Rusafa third, research sample intentionally chosen as school Radwan, and (30) students experimental group and (29) of control group, research tools were achievement test and the test of science operations and use the appropriate statistical tools to process information and data, showing results, the experimental group surpassed the control group in the collection and operations science, and light it, the researcher recommended several recommendat
... Show MoreThis research aimed to definite Blending learning (BL) technique, and to know the impact of its use onacademic achievement in Biology course of second class students in secondary special schools in Omdurman Locality and attitudes towards it, to achieve this; researcher adopted the experimental method. The sample was selected of (41) students, chosen from Atabiyah school, were divided into two equals groups: one experimental group reached (26) students studied by using the BL technique, and the second control group (25) students have been taught in the traditional method.
Data has collected by using two tools: achievement test and a questionnaire for measuring the attitudes towards Blend
... Show MoreThis research deals with study of the effect of additives on rheological properties (yield point, plastic viscosity ,and apparent viscosity) of emulsions. Twenty seven emulsion samples were prepared; all emulsions in this investigation are invert emulsions when water droplets are dispersed in diesel oil. The resulting emulsions are called water-in-oil (W/O) emulsions. The rheological properties of these emulsions were investigated using a couett coaxial cylinder rotational viscometer (Fann-VG model 35 A), by measuring shear stress versus shear rate. It was found that the effect of additives on rheological properties of emulsions as follow: the increase in the concentration of asphaltic material tends to increase the rheological propertie
... Show MoreA calculation have been carried out for determination some of the spectroscopic properties of Hydrogen Iodide HI molecules such as, the intensity of the absorption spectrum as a function of the variation of the temperature ranging from 10 to 1000 K. This study shows that the populations and hence intensity of the molecule increased as the temperature increased. Another determination of the maximum rotational quantum number Jmax of N2 , CO , BrF AgCl and HI molecules has been carried out.
Concrete is the main construction material of many structures. Exposing to loads creates cracks in concrete, which reduce the performance and durability. The decrease of concrete cracks becomes a necessity demand to ensure more durability and structural integrity of the concrete structure. Autogenous healing concrete is a kind of new smart concretes, which has the ability to reclose its cracks by means of itself. Concrete self-healing is a type of free repairs processes, which is reduce direct and indirect cost of maintenance and repairing. This work targets to inspect the mechanical properties of concrete after using two combinations of two materials (20 kg/m3 calcium hydroxide Ca(OH
The research’s main goal is to investigate the effects of using magnetic water in concrete mixes with regard to various mechanical properties such as compressive, flexural, and splitting tensile strength. The concrete mix investigated was designed to attain a specified cylinder compressive strength (30 MPa), with mix proportions of 1:1.8:2.68 cement to sand to crushed aggregate. The cement content was about 380 kg/m3, with a w/c ratio equal to 0.54, sand content of about 685 kg/m3, and gravel content of about 1,020 kg/m3. Magnetic water was prepared via passing ordinary water throughout a magnetic field with a magnetic intensity of 9,000 Gauss. The strength test
Porcelain is one of the most important ceramic materials with a wide range of traditional and technical applications. Since most mixtures of porcelain have a high sintering temperature, bentonite has been added in this research to improve the characteristics of sintering and burning. The porcelain mixture consisted of the following Iraqi raw materials: 30% wt kaolin, 30 wt% non-plastic clay (grog), 10% wt sodium feldspar, 10 wt% potassium feldspar and 20 wt% flint. After the mechanical mixing process and transfer the powder mixture to the slurry by adding distilled water, then different weight percentage of the sodium bentonite(0, 2.5, 5, 7.5 and 10) wt% was added. The specimens were prepared by using the solid casting m
... Show MoreAlginate from Large brown seaweeds act as natural polymer has been investigated as polymer and has been added to concrete in different percentages ( 0% , 0.5% , 1% and 1.5% ) by the cement weight and the study show the effect of using alginate biopolymer admixtures on some of the fresh properties of the concrete (slump & the density fresh) also in the hardened state ( Compressive strength , Splitting tensile strength and Flexural strength ) at 28 days. The mix proportion was (1:2.26:2.26) (cement: sand: gravel) respectively and at constant w/c equal to 0.47. The results indicate that the use of alginate as a percent of the cement weight possess a positive effect on fresh properties of co
... Show MoreThis research sheds light on the use of metal in the manufacture of jewelry, which is represented by ornamental tools in the period between the third and second millennium BC, in addition to the most important molds used in their manufacture. Man has been interested in metals since early ages, and was able to make tools that he uses in his daily life, especially jewelry. And the Syrian people got acquainted with the types of minerals, their characteristics, and how to deal with them. Minerals played an effective and prominent role in the economy of ancient Syria. Trade with those countries and secure their roads.