An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Hypergraphs with many Kneser colorings

For fixed positive integers r, k and E with 1 <= l < r and an r-uniform hypergraph H, let kappa(H, k, l) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l elements. Consider the function KC(n, r, k, l) = max(H epsilon Hn) kappa(H, k, l), where the maximum runs over the family H-n of all r-uniform hypergraphs on n vertices. In this paper, we determine the asymptotic behavior of the function KC(n, r, k, l) for every fixed r, k and l and describe the extremal hypergraphs. This variant of a problem of Erdos and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erdos-Ko-Rado Theorem (Erdos et al., 1961 [8]) on intersecting systems of sets. (C) 2011 Elsevier Ltd. All rights reserved.

Semilinear functional difference equations with infinite delay

We obtain boundedness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications to Volterra difference equations with infinite delay are shown. (C) 2011 Elsevier Ltd. All rights reserved.

Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.

Variations in Structure Explain the Viscometric Behavior of AOT Microemulsions at Low Water/AOT Molar Ratios

The viscosity of AOT/water/decane water-in-oil microemulsions exhibits a well-known maximum as a function of water/AOT molar ratio, which is usually attributed to increased attractions among nearly spherical droplets. The maximum can be removed by adding salt or by changing the oil to CCl4. Systematic small-angle X-ray scattering (SAXS) measurements have been used to monitor the structure of the microemulsion droplets in the composition regime where the maximum appears. On increasing the droplet concentration, the scattering intensity is found to scale with the inverse of the wavevector, a behavior which is consistent with cylindrical structures. The inverse wavevector scaling is not observed when the molar ratio is changed, moving the system away from the value corresponding to the viscosity maximum. It is also not present in the scattering from systems containing enough added salt to essentially eliminate the viscosity maximum. An asymptotic analysis of the SAXS data, complemented by some quantitative modeling, is consistent with cylindrical growth of droplets as their concentration is increased. Such elongated structures are familiar from related AOT systems in which the sodium counterion has been exchanged for a divalent one. However, the results of this study suggest that the formation of non-spherical aggregates at low molar ratios is an intrinsic property of AOT.