in this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. in particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.

The paper is concerned with the exponential attractors for viscoelastic wave model in $$\varOmega \subset \mathbb R^3$$ : $$\begin{aligned} u_{tt}-h_t(0)\varDelta u-\int _0^\infty \partial _sh_t(s)\varDelta u(t-s)\mathrm ds+f(u)=g, \end{aligned}$$ time-dependent memory kernel $$h_t(\cdot )$$ which used to aging phenomena of material. Conti et al. (Am J Math 140(2):349–389, 2018a; Am 140(6):1687...

To satisfy the performance specification and to have a good transient response of the system, the controlled system is often designed to possess a specific stability degree. If the controlled system has a stability degree  , we say that the system is exponentially stable. This paper gives sufficient condition for the exponential stability of linear discrete time delay systems. This new, delay-...

The concept of asymptotical stability is fundamental in the theory of ordinary and partial differential equations. In this way the stability theory leads to the real world applications. The recent advances of stability theory interact with spectral theory, harmonic analysis, modern topics of complex functions theory and also with control theory. This note begins with the following simple remark...

the gastric cancer in iran is the fourth in the general population. this study was designed to determine the five-year survival rate of gastric cancer patients, and to assess its associated factors. we analyzed the data using a time-dependent covariates model, and recommend it for analyses of similar data. 281 gastric cancer patients with adenocarcinomatous pathology who had been operated on at...