2 For example, 2-D affine models extend the rigid motion model by relaxing it into the following six-parameter linear model: (10)x′=ax+by+candy′=dx+ey+f. In addition to rigid transformations (scaling, rotation, and translation), an affine model can represent reflection, anisotropic ...
For a compact convex subset K of a locally convex space X, define A(K) to be the space of all continuous real-valued affine functions h on K, with supremum norm. It is clear that A(K) is uniformly closed subspace of C(K) and that it contains the subspace M of all functions of ...
It is defined as minimum hamming distance of any Boolean functionhfrom all affine functions. The mathematical expression for nonlinear of Boolean functionhis given as follows: $${\mathrm{NL}}_{h} ={\mathrm{min}}_{a\epsilon {A}_{n}}\mathrm{d}\left(h,a\right),$$ where\(a\epsilon {...
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...
For example, samples from different categories often overlap in the feature space, which may lead to a result that these samples can not truly reflect the accurate distribution of different categories. (2) The incompleteness data. This usually means that the training data cannot describe the real...
The transform property has several functions that allow elements to be transformed in two-dimensional or three-dimensional space. This proposal aims to add a new native CSS function that let you bend elements, using the following syntax:...
Molecular diversity of microglia, the resident immune cells in the CNS, is reported. Whether microglial subsets characterized by the expression of specific proteins constitute subtypes with distinct functions has not been fully elucidated. Here we descri
Then, the MPC problem is further solved by the projection neural network with different structures for the control of nonlinear affine systems [122–126], control of nonlinear systems [127–130], tracking control of underactuated vessels [131], synchronous control of barrel temperature for injection...
This is known as the “Serre–Swan Theorem” as it is proved for algebraic vector bundles over affine varieties by Serre [7] and for vector bundles over compact Hausdorff topological spaces by Swan [8]. The version for smooth vector bundles came into being at some point, and is given by...
In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting ...