Finite-Time Stability of Hybrid Systems With Unstable Modes

In this work, we study finite-time stability of hybrid systems with unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of a class of hybrid systems to be finite-time stable. More specifically, we show that even if the value of the Lyapunov function increases during continuous flow, i.e., if the unstable modes in the system are active for some time, finite-time stability can be guaranteed if the finite-time convergent mode is active for a sufficient amount of cumulative time. This is the first work on finite-time stability of hybrid systems using multiple Lyapunov functions. Prior work uses a common Lyapunov function approach, and requires the Lyapunov function to be decreasing during the continuous flows and non-increasing at the discrete jumps, thereby, restricting the hybrid system to only have stable modes, or to only evolve along the stable modes. In contrast, we allow Lyapunov functions to increase both during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the earlier results in the related literature, and in effect allow the hybrid system to have unstable modes.

DECODING SELF-PERSUASION IN VARIOUS PATHS OF CONNECTION IN PRAYER: AN APPROACH FROM THE PERSPECTIVE OF MARKETING IN THE ECCLESIASTICAL FIELD

"In marketing, the notion of persuasion may be depicted in campaigns based on continuous flows of consumer exposure to brand attributes. We believe that these attributes are melted in the conditioned responses of consumers towards the marketing of the brand. However, it is the brand associations triggered by consumers that constitute a premise for the business value of that brand. However, should we flip the approach of value from the consumer side, we consider that the embedding of the rand attributes may be related either to actual or ideal versions of self-concept. We propose to decode this embedding process by using self-persuasion as our guide and prayer as ommunication for our research realm."

On the Continuous Cancellative Semigroups on a Real Interval and on a Circle and Some Symmetry Issues

Let S denote the unit circle on the complex plane and ★:S2→S be a continuous binary, associative and cancellative operation. From some already known results, it can be deduced that the semigroup (S,★) is isomorphic to the group (S,·); thus, it is a group, where · is the usual multiplication of complex numbers. However, an elementary construction of such isomorphism has not been published so far. We present an elementary construction of all such continuous isomorphisms F from (S,·) into (S,★) and obtain, in this way, the following description of operation ★: x★y=F(F−1(x)·F−1(y)) for x,y∈S. We also provide some applications of that result and underline some symmetry issues, which arise between the consequences of it and of the analogous outcome for the real interval and which concern functional equations. In particular, we show how to use the result in the descriptions of the continuous flows and minimal homeomorphisms on S.

Continuous flows generate few homeomorphisms

We describe topological obstructions (involving periodic points, topological entropy and rotation sets) for a homeomorphism on a compact manifold to embed in a continuous flow. We prove that homeomorphisms in a $C^{0}$-open and dense set of homeomorphisms isotopic to the identity in compact manifolds of dimension at least two are not the time-1 map of a continuous flow. Such property is also true for volume-preserving homeomorphisms in compact manifolds of dimension at least five. In the case of conservative homeomorphisms of the torus $\mathbb {T}^{d} (d\ge 2)$ isotopic to identity, we describe necessary conditions for a homeomorphism to be flowable in terms of the rotation sets.

Microfluidic impedance cytometry device with N-shaped electrodes for lateral position measurement of single cells/particles

In this paper, we present an N-shaped electrode-based microfluidic impedance cytometry for the measurement of the lateral position of single cells and particles in continuous flows.