Affine [62–65] Nonlinear Polynomials [66,67] Thin-plate splines (TPS) [29,68,69] B-splines [56] Finite elements (meshes) [70–73] Mesh-free [26,28,74,75] Linear models represent deformation fields u=(u,v)T using linear functions (Section 4.1), while nonlinear models usually use ...
The typicality of the equation is that the last row [0 0 0 1] is omitted without a loss of generality as it is not needed in the subsequent calculations. The camera projects all such points in the world on its optical lens, which takes the form of an image using a projection through...
Miehe C, Göktepe S, Lulei F (2004) A micro-macro approach to rubber-like materials Part I: the non-affine micro-sphere model of rubber elasticity. Mech Phys Solids 52:2617–2660 Article Google Scholar Nguessong AN, Beda T, Peyraut F (2014) A new based error approach to approximate...
As an application, we obtain a removable singularity result for the linearized Monge–Ampère equation.doi:10.1007/s00229-015-0766-2LeDepartment of Mathematics, Indiana University, 831 E 3rd St, Bloomington, IN, 47405, USA;Nam Q.Department of Mathematics, Indiana University, 831 E 3rd St, ...
When the interval I k , i k involved in the definition of the affine map is half-open, the above equation needs to be interpreted in terms of the one-sided limit. For instance, when i k ∈ { 1 , 2 , ⋯ , N k − 1 } is odd, u k , i k ( x k , N k ) = x k...
First, we show the finite-time stability of system χ ˙ with the proposed controller ξ F T * ( χ ) and then prove the finite-time stability of the system (i.e., Equation (8)) with the proposed back-stepping controller (i.e., Equation (9)). The finite-time Lyapunov stability ...
The autonomic nervous system (ANS) is responsible for the precise regulation of tissue functions and organs and, thus, is crucial for optimal stress reactivity, adaptive responses and health in basic and challenged states (survival). The fine-tuning of c
Notice that if c1H = c1H+1, the model enforces dH = dH+1, which means that the two segments are affine with no discontinuity between (Qk e Qk+1); thus, rH can be chosen arbitrarily among these points. 3.1.2. PWL Model 2 The PWL model 2 has the same characteristics as Model 1 ...
Notice that we have the equation θ Q * * ( θ ) + Q ⋆ ( θ ) = 0 . Following the original construction of Amari’s Information Geometry [4], we have defined on the statistical bundle a manifold structure which is both an affine and a Riemannian manifold. The base manifold ε ...