In this work, we consider the nonlocal obstacle problem with a given $\psi$ in bounded Lipschitz domain $\Omega$ $\mathbb{R}^{d}$, such that $\mathbb{K}\_\psi^s={v\in H^s\_0(\Omega):v\geq\psi \text{ a.e. }\Omega}\neq\emptyset$, by $$ u\in\mathbb{K}\_\psi^s:\quad\langle\mathcal{L}au,v-u\rangle\geq\langle F,v-u\rangle\quad\forall v\in\mathbb{K}^s\psi, for $F$ $H^{-s}(\Omega)$, dual space of fract...

Abstract We establish several bounds on the cardinality of a topological space involving Hausdorff pseudocharacter $$H\psi (X)$$ H ψ ( X ) . This invariant has property $$\psi _c(X)\le H\psi (X)\le \chi <mml:...

The Cigler simple derivation of the q-Carlitz-Dobinski formula is recalled and it is noticed that the formula may be interpreted as the average of powers of random variable X q with the q-Poisson distribution. In parallel new q-Cigler-Dobinski and psi-Carlitz-Dobinski formulas are introduced. At first let us anticipate with ψ-remark. ψ denotes an extension of 1 n! n≥0 sequence to quite arbitrar...

Abstract The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior waves on black hole interiors with negative cosmological constant $$\Lambda &lt;0$$ Λ &lt; 0 explore consequences for Strong Cosmic...

In this note we show the somewhat surprising fact that proof of `if part' distinguished characterizations metric completeness due to Kirk, and Suzuki Takahashi, respectively, can be deduced in a straightforward manner from Hu's theorem space is complete if only any Banach contraction on bounded closed subsets thereof has fixed point. We also take advantage approach easily deduce characterizatio...

We provide an overview of the design of PSI (“a Private data Sharing Interface”), a system we are developing to enable researchers in the social sciences and other fields to share and explore privacy-sensitive datasets with the strong privacy protections of differential privacy. ∗This work is part of the “Privacy Tools for Sharing Research Data” project at Harvard, supported by NSF grant CNS-12...

We consider strongly degenerate parabolic operators of the form \[ \mathcal{L}:=\nabla_X\cdot(A(X,Y,t)\nabla_X)+X\cdot\nabla_Y-\partial_t \] in unbounded domains \Omega=\{(X,Y,t)=(x,x_{m},y,y_{m},t)\in\mathbb R^{m-1}\times\mathbb R\times\mathbb R\mid x_m>\psi(x,y,t)\}. assume that $A=A(X,Y,t)$ is bounded, measurable and uniformly elliptic (as a matrix $\mathbb R^{m}$) concerning $\psi$ $\Omega$...

let $g$ be a finite group‎. ‎we denote by $psi(g)$ the integer $sum_{gin g}o(g)$‎, ‎where $o(g)$ denotes the order of $g in g$‎. ‎here we show that‎ ‎$psi(a_5)< psi(g)$ for every non-simple group $g$ of order $60$‎, ‎where $a_5$ is the alternating group of degree $5$‎. ‎also we prove that $psi(psl(2,7))