are provided in cartesian coordinates or in direct coordinates (respectively fractional coordinates)....
Tolerance for each coordinate of a particular site. For example, [0.5, 0, 0.5] in cartesian coordinates will be considered to be on the same coordinates as [0, 0, 0] for a tolerance of 0.5. Defaults to 0.5. Returns: The most primitive structure found. The returned structure is guarant...
The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively. In particular, for v=m=1, the ...
The numerical method used is a mixed spectral element/Fourier spectral method developed for applications involving both Cartesian and cylindrical coordinates. In cylindrical coordinates, a formulation, based on special Jacobi-type polynomials, is used close to the axis of symmetry for the efficient ...
Consider the following fractional-order nonlinear model of a moving object in the cartesian coordinates: $$\left\{ {\begin{array}{*{20}{l}} {{D^a}x(t) = Ax(t) + \Phi (x(t))} \\ {y(t) = Cx(t)} \end{array}} \right.$$ ((32)) where a = 0.9 and $$\left\{ ...
and Gaussian-Hermite moments are examples of orthogonal moments in cartesian coordinates [4]. Orthogonal circular moments such as Mellin polar coordinate moments [5]. are defined over a unit disk using polar coordinates. These orthogonal circular moments are rotationally invariant where their magnitude ...
where \(\Delta x = x\left( t \right) - x(t - 1)\) and \(\Delta y = y\left( t \right) - y(t - 1)\), are the changes in the vector components of the cell movements in Cartesian coordinates at time t,Δt is the time step between different measurements of cell positions....
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Equation (6) can now be written in Cartesian coordinates as \begin{aligned} \bar{p}_{\mathrm{D1}}(r_{\mathrm{D}},s)= & {} \Big (\sqrt{(x_{\mathrm{D}}-\alpha _1)^2+(y_{\mathrm{D}}-\alpha _2)^2}\Big )^{\frac{1-\beta }{2}}\Bigg [A_1I_\nu \Big (\frac{...
These coordinates served as inputs to calculate the FD for α = [0.1; 1] with a step size of 0.1, resulting in ten different vectors for each processed exercise. It is important to note that with α = 1, we obtain a full derivative, representing the velocity of the pen tip. Due to...