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.
In this research, nanocomposites of poly(methyl methacrylate) (PMMA) and a mixture of nano silica (SiO2) and nano zirconia (ZrO2) were prepared in different weight percentages of the nano fillers to improve some of the properties of PMMA resin to be used as a denture base material. The nano filles were surface modified with a coupling agent and added to the PMMA in different amounts. Impact strength, transverse strength, hardness and roughness were tested for both control and experimental groups. The results indicate that PMMA/silica/zirconia nanocomposites, prepared with 5% by weight of both types of fillers, had a slight increase in impact s
In this study, reduced graphene oxide (rGO) was synthesized from graphene oxide (GO) via an ascorbic acid-assisted reduction process. GO was synthesized from graphite powder using a modified Hummers technique. The surface morphology, structure, functional groups, and elemental compositions of the produced materials were studied using various methods, such as scanning electron microscopy (SEM)/EDX, X-ray diffraction (XRD), atomic force microscopy (AFM), Fourier transform infrared (FTIR), and UV-Vis. The removal of oxygen-containing functional groups in rGO through reduction resulted in poor sample quality. In addition, FTIR investigations revealed that GO contained more oxygen-containing functional groups than rGO. Typical peaks at 2
... Show MoreThis paper describes the geotechnical properties of Al-Ammarah soil of Ammarah city in Messan Governorate-southern parts of Iraq. Data and other information taken from numbers of geotechnical reports that performed under the supervision of Consulting Engineering Bureau of Baghdad University. This research is devoted to study the correlation between different physical properties such as (LL, PI, LI, n,t, e) with different mechanical properties such as (qu, cc, cs, SPT). The correlation is verified using simple regression analysis. From the regression results it was found that there is direct correlation between different parameters. By using the correlation-with some information- preliminary investigation stages and studies of any s
... Show MoreThe assessment of data quality from different sources can be considered as a key challenge in supporting effective geospatial data integration and promoting collaboration in mapping projects. This paper presents a methodology for assessing positional and shape quality for authoritative large-scale data, such as Ordnance Survey (OS) UK data and General Directorate for Survey (GDS) Iraq data, and Volunteered Geographic Information (VGI), such as OpenStreetMap (OSM) data, with the intention of assessing possible integration. It is based on the measurement of discrepancies among the datasets, addressing positional accuracy and shape fidelity, using standard procedures and also directional statistics. Line feature comparison has been und
... Show MoreTo learn how the manner of preparation influences film development, this study examined film expansion under a variety of deposition settings. To learn about the membrane’s properties and to ascertain the optimal pretreatment conditions, which are represented by ambient temperature and pressure, Laser pressure of 2.5[Formula: see text]m bar, the laser energy density of 500[Formula: see text]mJ, distortion ratio ([Formula: see text]) as a function of laser pulse count, all achieved with the double-frequency Nd: YAG laser operating in quality-factor mode at 1064[Formula: see text]nm. MgxZn[Formula: see text] films of thickness [Formula: see text][Formula: see text]nm were deposited on glass substrates at pulse
... Show MoreAn electrolytic process for the removal of Zn(II) from aqueous solution using a parallel amalgamated copper screens cathode operated in the flow through mode is proposed. The current-potential curves recorded at a rotating amalgamated copper disc electrode were used to determine diffusion coefficient of Zn(II). The performance of electrolytic reactor was investigated by using different flow rates at initial zinc ion concentration(48 mg/L). Taking into account the residential Zn(II) concentration, the best results were obtained for cathode potential of (-1.35 V vs. SCE) at flow rate (320 L/h). Zinc ion concentration was found to decrease from 48 mg/L to 1 mg/L during 120 min. of electrolysis. The experimental data are well correlate
... Show MoreThe preparation of a new Azo compounds of highly conjugated dimeric and polymeric liquid crystal to achieve the crystalline characteristics Which have structures assigned based on elemental analysis, IR 1HNMR and CHNS-O while mesogenic properties have been set for DSC and hot-stage polarizing optical microscopy. The compounds show enantiotropicnematic phase being displayed. The compounds show photoluminescence properties in the organic solution at room temperature, with the fluorescence band centered around 400 nm.
Polypyrrole/silver (PPy/Ag) nanocomposites was synthesized via a chemical oxidative method. The AFM analysis is performed to study the surface roughness, morphology and size distribution of the PPy particles and PPy-ag nanocomposites. The results indicated that as the concentration of Ag in the nanocomposite increases, the roughness also increases. The size of nanoparticles was also evaluated and found in the range of 15 nm to 125 nm. The PPy/Ag nanocomposites exhibited an effectiveness against Gram-negative Escherichia coli showing an inhibition zone of 4mm and displayed poor efficacy against Gram-positive Staphylococcus aureus. Based on given adequate antibacterial characteristics of PPy/Ag nanocomposites, it can be identified as
... Show MoreThis work is divided into two parts first part study electronic structure and vibration properties of the Iobenguane material that is used in CT scan imaging. Iobenguane, or MIBG, is an aralkylguanidine analog of the adrenergic neurotransmitter norepinephrine and a radiopharmaceutical. It acts as a blocking agent for adrenergic neurons. When radiolabeled, it can be used in nuclear medicinal diagnostic techniques as well as in neuroendocrine antineoplastic treatments. The aim of this work is to provide general information about Iobenguane that can be used to obtain results to diagnose the diseases. The second part study image processing techniques, the CT scan image is transformed to frequency domain using the LWT. Two methods of contrast
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