Revista de Matemática Aplicada e Computacional

The Newton’s second law and third law has proven to be wrong, his mistake is the derivative operation the limitation resulting. Therefore new derivative the computation method desiderate the creation, this is the Inverse Derivative algorithm. The Inverse Derivative is a kind of extension of the derivative computation, it is based on the derivative calculated generated, using most of the derivative formulas to converted adjusted. In the field of physics and mechanical engineering, Inverse Derivative may be a large number of employed, to replace original derivative computation method. Will produce the enormous and profound influence.

This paper presents a simulation study of a finite Weibull mixture distribution (WMD) for modelling life data related to system components with different failure modes. The main aim of this study is to compare two analytical methods for estimating the parameters of WMD models, the maximum likelihood estimation (MLE) method using the expectation-maximization (EM) algorithm, [A1] and the non-linear median rank regression (NLMRR) method with the Levenberg-Marquardt algorithm. To perform this comparison, the Monte Carlo simulation technique is implemented to generate several replicates for complete failure data and censored data based on samples of different sizes that follow a two-component WMD. This study showed that MLE using the EM algorithm yields more accurate parameter estimates than the NLMRR method for small or moderate complete failure data samples. This method also converges faster than the NLMRR method for large samples that include censored data.

In this study, we outline the Kerner’s 3-phase traffic flow theory, which states that traffic flow occurs in three phases and these are free flow, synchronized flow and wide moving jam phases. A macroscopic traffic flow model that is factoring driver aggressiveness is developed and its features discussed. By construction of the solution to the Riemann problem, the model is written in conservative form and solved numerically. Using the Godunov numerical method we go ahead to simulate traffic flow on a multilane road with a lane-drop bottleneck. The model is compared with the Aw-Rascle model and features of the model are shown to reproduce the features of a three phase traffic flow which the Aw-Rascle model cannot reproduce. It is also shown that the model respects aspects of traffic by responding to frontal stimuli only and it does not produce negative travel.

This document is about Mathex, a software package that allows to embed Mathematica © macro expressions into a LaTeX document, combining together the power of the two systems. It works in this way: when You click F2 on your preferred editor, before of the TeX to PDF conversion, a pre-processor (written in the PERL language) call Mathematica, do the computation globally (i.e. treating the file as a single program) and replaces the macros in the final TeX. The macros should be inserted between the two conventional simbols <% ... %>, and can contain every valid Mathematica’s expression, or more espressions, separated by semicolon. As every expression and every graphics object get created everytime on-the-fly, the process can be slow.

The electronic properties of four new organic compounds (I-IV) were studied theoretically for application as hole-transporting materials in electroluminescent (EL) devices. We investigated theoretically, the effect of increasing number of pyrrole rings between 4-azainole end moieties. The time dependent density functional theory (TD-DFT/ B3LYP/6-31G(d)) calculated energy gap (E-gap) of the studied compounds decreases in the order of I>II>III>IV; the significant reduction of E-gap of compound IV with 2.7 eV compared to 4.27 eV of compound II is due to the bridging effect of C=C(CO2H)2 which remove the steric effect, caused by high dihedral angle between two central pyrrole rings in the non-bridged II. Compound IV possess low-lying lowest occupied molecular orbital(LUMO) energy levels and low lying highest occupied molecular orbital (HOMO) energy levels, may be promising candidate for hole transporting and bright blue to red emitting layer in organic light emitting device (OLED) fabrication.