Related papers: Necessary and sufficient condition for stability o…
q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general,…
In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a…
A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient…
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation valu of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…
Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is…
Necessary and sufficient conditions for the existence of a composite-system statistical operator, and, separately, for the possibility of its being correlated or uncorrelated, are derived in terms of its range dimension and the range…