We consider embeddings of graphs in the 3-space R (all embeddings inthis paper are assumed to be piecewise linear). An embbeding of a graph in R3 is linkless if every pair of disjoint cycles forms a trivial link (in the senseof knot theory), i.e., each of the two cycles (in R) can be embedded in aclosed topological 2-disk disjoint from the other cycle. Robertson, Seymour and...

To facilitate the damping matching of dampers for vehicle passive suspensions, this paper proposes an analytical matching method of the optimal piecewise linear damping characteristics curve. Based on the vehicle vibration model, taking the suspension dynamic deflection as the constraint, by the vibration acceleration and the wheel dynamic load, an objective function about the relative damping ...

In this paper we will develop a theory for simplicial diffeomorphims, that is, diffeomorphims that preserve the incidence relations of a simplicial complex, and analyze alternative schemes to construct them with different properties. In combining piecewise linear functions on complexes with simplicial diffeomorphisms, we propose a new representation of curves and surfaces (and hypersurfaces, in...

This paper studies a mathematical basis of piecewise linear approximation in the L1 optimal control problem of sampled-data systems, which aims at minimizing the L∞induced norm of sampled-data systems. To take into account of intersample behavior, we first consider the lifted representation of sampled-data systems. The sampling interval [0, h) is then divided into M subintervals with an equal w...

In this paper, is proposed a method to implement in FPGA (Field Programmable Gate Array) circuits different approximation of the sigmoid function. Three previously published piecewise linear and one piecewise second-order approximation are analyzed from point of view of hardware resources utilization, induced errors caused by the approximation function and bits representation, power consumption...

System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a speci...

The model of adaptive hinging hyperplanes (AHH) is proposed in this paper for black-box modeling. It is based on Multivariate Adaptive Regression Splines (MARS) and Generalized Hinging Hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subarea. It is proved that AHH model is identical to a spec...

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article propos...

This paper investigates the topology of piecewise linear scalar functions, such as the interpolation function over a tetrahedralized volumetric grid. An algorithm is presented that creates a hierarchical representation of a Morse-Smale complex based on persistence. We show the correctness of our approach and discuss the applications. 1