Narrow Results

Considering that a mechanical spring can be compressed or stretched only, a protected object is prone to detach from the support spring when the system falls into the resonant region. To avoid this phenomenon, a nonlinear vibration isolator containing a viscoelastic end-stop buffer is developed, which can exhibit stiffness–hardening or stiffness–softening characteristics. Because the restoring force is asymmetrical and piecewise linear, a modified averaging method is applied to obtain steady-state solutions, which contain a bias term. A numerical method is then used to verify the analytical solutions, and their stability is determined. Finally, the effects of the structural parameters on the frequency response and force transmissibility are investigated. The jump avoidance condition is subsequently given. The results show that the modified averaging method is more accurate than the classical method. Decreasing the stiffness ratio can reduce the transmissibility peak and resonance frequency. Applying heavy damping in the end-stop buffer is beneficial for reducing transmissibility in the resonant region, whereas the isolation performance at high frequencies remains unchanged. The developed vibration system exhibits better isolation performance than the linear system when stiffness–softening characteristics are considered.

Multicommodity network problems appear in numerous applications, such as telecommunications, logistics, transportation, distribution and production planning networks. The piecewise linear multicommodity network flow problem is a multicommodity network flow problem with piecewise linear costs corresponding to multiple resources, such as communication lines, vehicles and production lines. In the present paper, for the piecewise linear multicommodity network continuous flow problem, we present a path-based formulation and an arc-based formulation, and develop a combined matheuristic approach, which combines capacity scaling, a column and row generation technique, restricted branch-and-bound and a local branch method.

In this paper n-double scroll generating via diode-based PieceWise-Linear (PWL) circuit in State Controlled Cellular Neural Network (SC-CNN) is presented. It has been shown that by using simple diode-based configurations; alternative nonlinear circuit configurations for chaotic circuits and PWL-based systems can be used in the generation of n-double scrolls. With this study, while the analysis of the nonlinear block in the SC-CNN-based circuit is simplified, the implementation cost of the circuit is also reduced. Pspice simulations are proved with experimental studies.

In this paper, we consider a class of flux controlled memristive circuits with a piecewise linear memristor (i.e. the characteristic curve of the memristor is given by a piecewise linear function). The mathematical model is described by a discontinuous planar piecewise smooth differential system, which is defined on three zones separated by two parallel straight lines $\left|x\right|=1$ (called as discontinuity lines in discontinuous differential systems). We first investigate the stability of equilibrium points and the existence and uniqueness of a crossing limit cycle for the memristor-based circuit under self-excited oscillation. We then analyze the existence of periodic orbits of forced nonlinear oscillation for the memristive circuit with an external exciting source. Finally, we give numerical simulations to show good matches between our theoretical and simulation results.

Suppose P_n is a regular n-gon in ℝ². An embedding f : P_n ↪ ℝ³ is called an α-regular stick knot provided the image of each side of P_n under f is a line segment of length 1 and any two consecutive line segments meet at an angle of α. The main result of this paper proves the existence of α-regular stick unknots for odd n ≥ 7 with α in the range . All knots constructed will have trivial knot type, and we will show that any non-trivial α-regular stick knot must have .

We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in the group is a union of a family of quantifier free definable sets, where the parameter of the family runs over a set definable (with quantifiers) in a sort which carries the structure of an ordered set with some additional unary predicates.

As a corollary, we find that all definable functions in ordered abelian groups are piecewise linear on finitely many definable pieces.