The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
Image recognition is one of the most important applications of information processing, in this paper; a comparison between 3-level techniques based image recognition has been achieved, using discrete wavelet (DWT) and stationary wavelet transforms (SWT), stationary-stationary-stationary (sss), stationary-stationary-wavelet (ssw), stationary-wavelet-stationary (sws), stationary-wavelet-wavelet (sww), wavelet-stationary- stationary (wss), wavelet-stationary-wavelet (wsw), wavelet-wavelet-stationary (wws) and wavelet-wavelet-wavelet (www). A comparison between these techniques has been implemented. according to the peak signal to noise ratio (PSNR), root mean square error (RMSE), compression ratio (CR) and the coding noise e (n) of each third
... Show MoreThe consensus algorithm is the core mechanism of blockchain and is used to ensure data consistency among blockchain nodes. The PBFT consensus algorithm is widely used in alliance chains because it is resistant to Byzantine errors. However, the present PBFT (Practical Byzantine Fault Tolerance) still has issues with master node selection that is random and complicated communication. The IBFT consensus technique, which is enhanced, is proposed in this study and is based on node trust value and BLS (Boneh-Lynn-Shacham) aggregate signature. In IBFT, multi-level indicators are used to calculate the trust value of each node, and some nodes are selected to take part in network consensus as a result of this calculation. The master node is chosen
... Show More- Epstein, B., and sobel , M. (1954)."Some Thearems Relevant to life Testing from an Exponential population" Annals of Mathematical Statistics, 25, 373 – 381 .
- Epstein, B., and Tsao, C.K.(1953) "Some Tests Based on Order Observation From Two Exponential Populations" Annals of Mathematical Statistics , 24 , 458 – 466 .
- Hogg, R.V. and Tonis, E,A. (1963), "An Iterated procedure for Testing the Equality of several Exponential Distributions" Journal of the American Statistical Association, 58 , 435 – 443.
- Kumar, S. , and patel , H. I. (1971) "ATest for the Comparision of two Exponential Disributions" Technometrics , 13 , 183 – 189 .<
This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie
... Show MoreThe simulation of passively Q-switching is four non – linear first order differential equations. The optimization of passively Q-switching simulation was carried out using the constrained Rosenbrock technique. The maximization option in this technique was utilized to the fourth equation as an objective function; the parameters, γa, γc and β as were dealt with as decision variables. A FORTRAN program was written to determine the optimum values of the decision variables through the simulation of the four coupled equations, for ruby laser Q–switched by Dy +2: CaF2.For different Dy +2:CaF2 molecules number, the values of decision variables was predicted using our written program. The relaxation time of Dy +2: CaF2, used with ruby was
... Show MoreA total of nine swab samples were collected from inflamed teeth and gingiva of human’soral cavity from a dentist clinic in Baghdad. All specimens were cultured in Mitis Salivarius agar medium and the isolated bacterial pure colonies werethen identified by using VITEK2. Three samples were diagnosed and identified as Staphylococcus lentus. One of the three isolates which showed a distinctive heavy growth on the media was selected for further analysis in this study. Paper disk diffusion method was used to detect the antibacterial activityof three of mouthwash solutions (Zak, Colgate and Listerine). The results showed that “Colgate†was the most active solution with antibacterial activity compared with the other two s
... Show MoreDensities ρ and viscosities η for several concentrations of amino acids (Serine, Cysteine and Threonine) at different temperatures (298.15, 303.15 and 308.15K) have been measured. On the basis of these data, the apparent molal volumes v , partial molal volumes at infinite dilution v , slope Sv , Gibbs free energy of activation for viscous flow of solution ∆G1,2 and Jones – Dole Bcoefficients were calculated the nature of solute-solvent and solute-solute interactions have been discussed in terms of the values of v , v , Sv and B-coefficents
