As part of global climate change an accelerated hydrologic cycle (including an increase in heavy precipitation) is anticipated (Trenberth \cite{trenb1, trenb2}). So, it is of great importance to be able to quantify high-impact hydrologic relationships, for example, the impact that an extreme precipitation (or temperature) in a location has on a surrounding region. Building on the Multivariate Extreme Value Theory we propose a contagion index and a stability index. The contagion index makes it possible to quantify the effect that an exceedance above a high threshold can have on a region. The stability index reflects the expected number of crossings of a high threshold in a region associated to a specific location i, given the occurrence of at least one crossing at that location. We will find some relations with well-known extremal dependence measures found in the literature, which will provide immediate estimators. For these estimators an application to the annual maxima precipitation in Portuguese regions is presented.
The following time delay system x˙ = Ax(t) +∑r 1 bq∗ i x(t − τi) − bϕ(c ∗ x(t)) is considered, where ϕ: ℝ → ℝ may have discontinuities, in particular at the origin. The solution is defined using the ''redefined nonlinearity'' concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.
A singularly perturbed linear time-invariant time delay controlled system is considered. The singular perturbations are subject to the presence of two small positive multipliers for some of the derivatives in the system. These multipliers (the parameters of singular perturbations) are of different orders of the smallness. The delay in the slow state variable is non-small (of order of 1). The delays in the fast state variables are proportional to the corresponding parameters of singular perturbations. Three much simpler parameters-free subsystems are associated with the original system. It is established that the exponential stability of the unforced versions of these subsystems yields the exponential stability of the unforced version of the original system uniformly in the parameters of singular perturbations. It also is shown that the stabilization of the parameters-free subsystems by memory-free state-feedback controls yields the stabilization of the original system by a memory-free state-feedback control uniformly in the parameters of singular perturbations. Illustrative examples are presented.
In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. The results of this paper extend those in the literature. Numerical examples are given to illustrate the presented results.
We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1,X2,… when testing two simple hypotheses about their common density f: f=f0 versus f=f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by X1,X2,… with the density f0. For τ∗ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between f0 and an alternative f~1, where f~1 is some approximation to f1. An inequality is obtained which gives an upper bound for the expected cost excess, when τ∗ is used instead of the rule τ~∗ optimal for the pair (f0,f~1). The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs (f0,f1) and (f0,f~1).
We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space X. It is supposed that an unknown transition probability p(⋅|x), x∈X, is approximated by the transition probability p˜(⋅|x), x∈X, and the stopping rule τ˜∗, optimal for p˜, is applied to the process governed by p. We found an upper bound for the difference between the total expected cost, resulting when applying \wtτ∗, and the minimal total expected cost. The bound given is a constant times \dpssupx∈X∥p(⋅|x)−\wtp(⋅|x)∥, where ∥⋅∥is the total variation norm.
A one-dimensional version of a gradient system, known as ''Kobayashi-Warren-Carter system'', is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a ''stability'' which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further, this is specified by using the notion of ''energy-dissipative solution'', proposed in a relevant previous work.
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $$ ({\rm P}) \begin {cases} \dot {u}(t)+A(t)u(t)=f(t)\quad t\text {-a.e. on} [0,\tau ], u(0)=0, \end {cases} $$ where $A\colon [0,\tau ]\to \mathcal {L}(X,D)$ is a bounded and strongly measurable function and $X$, $D$ are Banach spaces such that $D\underset {d}\to {\hookrightarrow }X$. Our main concern is to characterize $L^p$-maximal regularity and to give an explicit approximation of the problem (P).
In this paper we use the fixed point method to prove asymptotic stability results of the zero solution of a generalized linear neutral difference equation with variable delays. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Y. N. Raffoul (2006), E. Yankson (2009), M. Islam and E. Yankson (2005).
A frequently used technological solution of reducing the time varying forces transmitted between the rotor and its casing is represented by application of a flexible suspension with damping devices added to the constraint elements. To achieve their optimum performance their damping effect must be controllable. For this purpose a concept of a hybrid damping device working on the principle of squeezing the layers of normal and magnetorheological oils have been developed. Here in this article, there is investigated influence of the proposed damping element on stabilty of the rotor vibrations induced by its imbalance during the steady state operating regimes. The stability is assessed by the evolutive method which is based on evaluation of eigenvalues of the system linearized in a small neighbourhood of the rotor phase trajectory and calculation of the corresponding damping ratio or logarithmic decrement. and Obsahuje seznam literatury