Sentence examples for coordinate variables from inspiring English sources

Expressing the unknown in terms of the polar coordinate variables r and θ, he showed that a solution of the polynomial would lie at the intersection of two curves of the form T r, θ) = 0 and U r, θ) = 0.

These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface.

On changing coordinate variables, using the Hooke and Jevees pattern search algorithm, the member areas are treated as dependent design variables.

Because the properties of Cartesian and curvilinear grids differ whether the coupling of the coordinate variables between the physical and computational domains exists or not, different mathematical formulations are developed for each grid type.

We follow the work in Fatemi and Odeh [9] and in Majorana and Pidatella [16] to formulate the Boltzmann Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms.

Since PCA is based on mean-centered data, and the PCs, themselves, are linear combinations of the original coordinate variables, one can construct the configuration at a specific point in PC space by simply multiplying the coefficients for the linear combination of coordinates represented by each PC of interest by the coordinate of the point of interest on that PC.

The material properties are assumed varying as a power form of thickness coordinate variable.

Let be a function satisfying the following: for all ; is affine in the first coordinate variable; for each fixed, is sequentially continuous from the weak topology to the weak topology.

where c and m index designate the ceramic and the metal, respectively, n is the exponent of the volume fraction (n ≥ 0), z is the thickness coordinate variable, E elastic modulus, ρ mass density, h is the thickness of the plate and ν is the Poisson's ratio.

The messages in the nodes A θ and B θ are finally converted to the coordinate variable node, as[6 8] begin{array}rcl@ left(m_{A_{theta} rightarrow Delta x_{theta} },sigma^{2}_{A_{theta} rightarrow Delta x_{theta} }right)=left X-m_{x rightarrow A_{theta}},sigma^{2}_{x rightarrow A_{theta}}right), end{array} (18).

A linearizing robust dynamic output feedback control scheme is proposed for earth coordinate position variables trajectory tracking tasks in a hovercraft vessel model.