We here provide two sided bounds for the density of the solution of a system of n di erential equations of dimension d, the rst one being forced by a non-degenerate random noise and the n− 1 other ones being degenerate. The system formed by the n equations satis es a suitable Hörmander condition: the second equation feels the noise plugged into the rst equation, the third equation feels the noi...

Lipschitz domains. Our presentations here will almost exclusively be for bounded Lipschitz domains. Roughly speaking, a domain (a connected open set) Ω ⊂ R is called a Lipschitz domain if its boundary ∂Ω can be locally represented by Lipschitz continuous function; namely for any x ∈ ∂Ω, there exists a neighborhood of x, G ⊂ R, such that G ∩ ∂Ω is the graph of a Lipschitz continuous function und...

We give conditions that ensure an operator satisfying a Piestch domination in given setting also satisfies different setting. From this we derive bounded multilinear T T </mml:semant...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

This article discusses Lipschitz properties of generated aggrega-tion functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provid...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

colorectal cancer is the second leading cause of cancer death worldwide. through risk assessment of malignancy in polyps, screening programs can achieve the best results. this study aimed to determine the association between the grade of dysplasia and the location of colorectal polyps. 240 colorectal adenomatous polyps which were referred to department of pathology at rasoul-e-akram hospital be...

We consider the setting of stochastic bandit problems with a continuum of arms indexed by [0, 1]. We first point out that the strategies considered so far in the literature only provided theoretical guarantees of the form: given some tuning parameters, the regret is small with respect to a class of environments that depends on these parameters. This is however not the right perspective, as it i...

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class parabolic semilinear stochastic partial differential equations driven by additive noise, under one-sided Lipschitz continuity condition. The setting encompasses nonlinearities with polynomial growth. First, we prove that moment bounds for numerical hold, at most dependence respect time horizon. S...