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.
ABSTRACTObjective: The objective of this study is to develop a controlled release matrix tablet of candesartan cilexetil to reduce the frequency of administration,enhance bioavailability and improve patient compliance; a once daily sustained release formulation of candesartan cilexetil is desirable.Methods: The prepared tablets from F1 to F24 were evaluated with different evaluation parameters like weight variation, drug content, friability,hardness, thickness and swelling ability. In vitro release for all formulas were studied depends on the type and amount of each polymer, i.e. (16 mg,32 mg and 48 mg) respectively beside to the combination effect of polymers on the release of the drug from the tablet.Results: In vitro release show
... Show MoreThe pure and Sb doped GeSe thin films have been prepared by thermal flash evaporation technique. Both the structural and optical measurement were carried out for as deposited and annealed films at different annealing temperatures.XRD spectra revealed that the all films have one significant broad amorphous peak except for pure GeSe thin film which annealed at 573 K, it has sharp peak belong to orthorhombic structure nearly at 2θ=33o. The results of the optical studies showed that the optical transition is direct and indirect allowed. The energy gap in general increased with increasing annealing temperature and decreased with increase the ratio of Sb dopant. The optical parameters such as refractive index, extinction coefficient and real and
... Show MoreIn this study, pure SnO2 Nanoparticles doped with Cu were synthesized by a chemical precipitation method. Using SnCl2.2H2O, CuCl2.2H2O as raw materials, the materials were annealed at 550°C for 3 hours in order to improve crystallization. The XRD results showed that the samples crystallized in the tetragonal rutile type SnO2 stage. As the average SnO2 crystal size is pure 9nm and varies with the change of Cu doping (0.5%, 1%, 1.5%, 2%, 2.5%, 3%),( 8.35, 8.36, 8.67, 9 ,7, 8.86)nm respectively an increase in crystal size to 2.5% decreases at this rate and that the crystal of SnO2 does not change with the introduction of Cu, and S
... Show MoreIn this work, the effect of anodizing duration on the morphology and photoelectrochemical properties of TiO2 nanotubes arrays (NTAs) has been investigated The samples were characterized by X-ray diffraction (XRD) and energy dispersive X-ray (EDX) to characterize their crystalline structure and compositional. Surface morphological and their dimensional variation was examined by field emission scanning electron microscopy (FESEM). The anodizing duration played a significant role in the formation of TiO2 nanotubes arrays. Moreover, the photoelectrochemical properties (PEC) were studied through photocurrent measurements. Optimum anodizing duration of 60 min at 40 V exhibited maximum photocurrent of 0.03 mA cm-2 under illumination of hal
... Show MoreBackground: Colonization of soft denture liners by Candida albicans and other microorganisms continued to be a serious problem. The aim of this study was to evaluate the effect of incorporating silver nanoparticles into heat cured acrylic-based soft denture liner on the antifungal activity, and on water sorption, solubility, shear bond strength and color change of the soft lining material. Furthermore, evaluating the amount of silver released. Materials and methods: Silver nanoparticles were incorporated into soft denture liner in different percentages (0.05%, 0.1% and 0.2% by weight). Four hundred and twenty specimens were prepared and divided into five groups according to the test to be performed. The antifungal activity of the soft liner
... Show MoreThe present work involves studying the effect of electrolyte composition [@1= 0.5 wt.% NH4F / 5% H2O / 5% Glycerol (GLY)/ 90% Ethylene Glycol (EG)] and [ @2= 0.5 wt. % NH4F / 5% H2O / 95% Ethylene Glycol (EG)] on the structural and photoelectrochemical properties of titania nanotubes arrays (TNTAs). TNTAs substrates were successfully carried out via anodization technique and were carried out in 40 V for one hour in different electrolytes (@1, and @2). The properties of physicochemical of TNTAs were distinguished via an X-ray Diffractometer (XRD), Field Emission Scanning Electron Microscope (FESEM), an Energy Dispersive X-ray (EDX), and UV–visible diffuse reflectance. The photoelectrochemical response of TNTAs was evaluated
... Show MoreIn this work, The effect of annealing treatment at different temperatures (373, 423 and 473) K and chemical treatment with talwen at different immersion time (40, 60 and 80) min on structural and optical properties of the bulk heterojunction (BHJ) blend copper phthalocyanine tetrasulfonic acid tetrasodium salt/poly dioxyethylenethienylene doped with polystyrenesulphonic acid (CuPcTs/PEDOT:PSS) thin films were investigated. The films were fabricated using spin coating technique. X-ray diffraction (XRD) measurements displayed only one peak at 2θ =4.5o corresponding to (001) direction which has dhkl larger than for standard CuPcTs. The dhkl increase then decrease with increasing annealing temperature and
the time of chemical treatment w
Present study was conducted in order to assess Slabiaat water quality by measuring some physical and chemical factors of river water, the study included a choice of three stations along of Slabiaat River in Samawa city, water samples collected a monthly during the period from September 2013 August 2014. The study involved measuring the Air & water temperatures, pH, Electrical conductivity, Total dissolved solids, Dissolved oxygen, Total hardness, calcium hardness, magnesium, turbidity, and some types of bacteria in River water. The study results showed that the values of air & water temperatures have ranged between (20.1-36.6)?C , (10-21.8) in Slabiaat River, respectively . pH values ranged between (6.6-8.7). Electrical conductivity in
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