This paper is concerned with efficient integration of bilinear H∞ control and adaptive inverse control to attain vibration isolation of structure installed with a semi-active MR damper in which its damping force is controllable by input voltage. The structure with MR damper is expressed by a bilinear dynamic equation. The role of the bilinear H∞ controller is to provide the desired damping forc...

In this paper, we consider linear stability issues for one-dimensional hyperbolic conservation laws using a class of conservative high order upwind-biased finite difference schemes, which is a prototype for the weighted essentially non-oscillatory (WENO) schemes, for initial-boundary value problems (IBVP). The inflow boundary is treated by the so-called inverse Lax-Wendroff (ILW) or simplified ...

We introduce a family of first-order multidimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion equ...

In this work we apply non-negative matrix factorizations (NMF) to some imaging and inverse problems. We propose a sparse low-rank approximation of big data and images in terms of tensor products, and investigate its effectiveness in terms of the number of tensor products to be used in the approximation. A multi-resolution analysis (MRA) framework is presented using a sparse low-rank approximati...

In this paper, we extend previous results on average commute-times for undirected graphs to fully-connected directed graphs, corresponding to irreducible Markov chains. We introduce an unsymmetrized generalized Laplacian matrix and show how its pseudo-inverse directly yields the one-way first-transit times and round-trip commute times with formulas almost matching those for the undirected graph...

Surface wave method can be used to determine the properties of the component materials of a pavement structure. The measurements are made of the differences in the phase of a wave of the Rayleigh type, received at two points at known radial spacing from the source of the wave. Pavements for highways or airport runways are usually constructed of cement concrete. Such pavements are treated as a s...

To compensate for missing functions of lower extremity amputees, this paper proposes a model of an intelligent bionic leg semi-actively controlled by a magnetorheological damper (MRD). A mechanical structure of the leg is designed, and with the help of Bouc-Wen model, a MRD forward dynamics model is constructed for simulation. On the basis of data obtained from simulations, the MRD inverse dyna...

We study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient. Let {pn}n=0 be a sequence of orthonormal polynomials and pn+ the restriction of pn to [an,∞), where an is the maximum zero of pn. Then p −1 n+ and the composite pn−1 ◦ p −1 n+ are operator monotone on [0,∞). Furthermore, for every polynomial p with a positive leading coefficient there is a...

We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) ‘admissible’ measures whose convolution results in a so-called ‘invertible measure’ which is either a smoothly-decaying measure supported on the entire real line (such as th...