In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained for each subpopulation as a vector distribution. The numerical outputs are tabulated, graphed, and compared with previous statistical estimations for 2013, 2015, and 2030, respectively. The solutions of FD and MMCFD are found to be in good agreement with small standard deviation of the means, and small measure of difference. The new MMCFD method is useful to predict intervals of random distributions for the numerical solutions of this epidemiology model with better approximation and agreement between existing statistical estimations and FD numerical solutions.
In this work a model of a source generating truly random quadrature phase shift keying (QPSK) signal constellation required for quantum key distribution (QKD) system based on BB84 protocol using phase coding is implemented by using the software package OPTISYSTEM9. The randomness of the sequence generated is achieved by building an optical setup based on a weak laser source, beam splitters and single-photon avalanche photodiodes operating in Geiger mode. The random string obtained from the optical setup is used to generate the quadrature phase shift keying signal constellation required for phase coding in quantum key distribution system based on BB84 protocol with a bit rate of 2GHz/s.
Solutions of dyes Rhodamine 6G (Rh6G) and Coumarin480(C480) were prepared at five concentrations (1x10-3, 5x10-4, 1x10-4, 5x10-5 and1x10-5) mol/l, the mixing was stirred to obtain on a homogenous solution, the(poly methyl-methacrylate) (PMMA) was solved by chloroform solvent with certain ratio, afterward (PMMA+Rh6G) and (PMMA+C480) thin films were prepared by casting method on glass block which has substrate with dimensions (7.5 x2.5)cm2, the prepared samples were left in dark place at room temperature for 24 hours to obtain uniform and homogenous thin films. UV-VIS absorption spectra, transmission spectra and fluorescence spectra were done to measure linear refractive index and linear absorption coefficient. The nonlinear optical proper
... Show MoreA huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the mat
... Show Morein this article, we present a definition of k-generalized map independent of non-expansive map and give infinite families of non-expansive and k-generalized maps new iterative algorithms. Such algorithms are also studied in the Hilbert spaces as the potential to exist for asymptotic common fixed point.
This paper proposes a new structure of the hybrid neural controller based on the identification model for nonlinear systems. The goal of this work is to employ the structure of the Modified Elman Neural Network (MENN) model into the NARMA-L2 structure instead of Multi-Layer Perceptron (MLP) model in order to construct a new hybrid neural structure that can be used as an identifier model and a nonlinear controller for the SISO linear or nonlinear systems. Weight parameters of the hybrid neural structure with its serial-parallel configuration are adapted by using the Back propagation learning algorithm. The ability of the proposed hybrid neural structure for nonlinear system has achieved a fast learning with minimum number
... Show MoreMany of the key stream generators which are used in practice are LFSR-based in the sense that they produce the key stream according to a rule y = C(L(x)), where L(x) denotes an internal linear bit stream, produced by small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. In this paper we combine between the output sequences from the linear feedback shift registers with the sequences out from non linear key generator to get the final very strong key sequence
The increasing demand for energy has encouraged the development of renewable resources and environmentally benign fuel such as biodiesel. In this study, ethyl fatty esters (EFEs), a major component of biodiesel fuel, were synthesized from soybean oil using sodium ethoxide as a catalyst. By-products were glycerol and difatty acyl urea (DFAU), which has biological characteristics, as antibiotics and antifungal medications. Both EFEs and DFAU have been characterized using Fourier transform infrared (FTIR) spectroscopy, and 1H nuclear magnetic resonance (NMR) technique. The optimum conditions were studied as a function of reaction time, reactant molar ratios, catalyst percentage and the effect of organic solvents. The conversion ratio of soybea
... Show MoreThe Cu(II) was found using a quick and uncomplicated procedure that involved reacting it with a freshly synthesized ligand to create an orange complex that had an absorbance peak of 481.5 nm in an acidic solution. The best conditions for the formation of the complex were studied from the concentration of the ligand, medium, the eff ect of the addition sequence, the eff ect of temperature, and the time of complex formation. The results obtained are scatter plot extending from 0.1–9 ppm and a linear range from 0.1–7 ppm. Relative standard deviation (RSD%) for n = 8 is less than 0.5, recovery % (R%) within acceptable values, correlation coeffi cient (r) equal 0.9986, coeffi cient of determination (r2) equal to 0.9973, and percentage capita
... Show MoreThis paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.