The new Euler–Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain
24 proposed a modular approach for facial expression recognition using Euler principal component analysis (PCA). This approach reduces the influence of illumination on image content to a certain extent, while PCA-based method suffers from a problem that the projection maximizes the variance of all ...
Another important formula is Euler’s reflection formula $$\begin{aligned} \Gamma (1-x)\Gamma (x)=\frac{\pi }{\sin (\pi x)},\quad 0<x<1. \end{aligned}$$ (1.2) In this paper, we investigate some ratios of the Pochhammer k-symbol...
In this article, an improved approach for editing color images has been presented. In this approach, using the Poisson equation, a guided vector field is created by employing source and target images within a selected region at the first step. Next, the
This method, however, introduces computational complexity into the solution as it requires the solution of an implicit equation, to determine the point of transition between the two regions. Recently, an extended Mohr–Coulomb model was developed (Shafiq and Subhash, 2016a) to capture the nonlinear...
This hyperbolic system is then solved numerically via conservative method:(4)Qin+1=Qin−ΔtΔx[Fi+1/2−Fi−1/2]−ΔtΔy[Gj+1/2−Gj−1/2]with the numerical flux Fi+1/2 and Gj+1/2. 2.2. AUSM-family schemes Based on the rotational invariance property of Euler equations [...
The differential Eq. (5) is indeed solved using Scilab software and the explicit Euler method, first with initial guesses of the unknown convec- tion coefficients hi and he,pl . Then the Scilab routine 'data- fit' is applied, which consists to minimize the sum over the experiment ...
(9) Position error equations: δλ = sec L RN δ L δ vEn = + δ vNn RM vEn sec L RN tan L δ L (10) where superscript n′ donates the calculation navigation reference frame, and φ = φx φy φz T is t...
The overall discrete form (discretized by the forward Euler method) was given as in Eq. 23, however that does not suits to the general state-space model, where the state vector xk has to be updated in each and every step. In order to make these two forms equally, one has to ...
The above formula was derived from the arm base coordinate frame (for example, coordinate frame OLXLYLZL for left arm). The force/moment balance equation of joint i can be obtained by combining the Newton Euler method and screw theory, as shown in the following equation: (8) Equation (8...