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We show decay estimates for the propagator of the discrete Schrödinger and Klein–Gordon equations in the form {{\| {U(t)f} \|}_{{l^\infty}}} \leq C (1+|t|)^{-d/3}{{\| {f} \|}_{{l^1}}} . This impl...
We develop a theory of perverse sheaves on the semi-infinite flag manifold G((t))/N((t)) · T[[t]], and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular bloc...
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M⩾3 sites, using as a prototypical example the discrete nonlinear Schrödinger equation...
Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schr¨odinger equation with septic and higher power-law nonlinearities and an external potenti...
There has been recent growth in small area estimation due to the need for more precise estimation of small geographic areas, which has led to groups such as the U.S. Census Bureau, Google, and the RAN...
The Fay-Herriot (FH) model is widely used in small area estimation and uses auxiliary information to reduce estimation variance at undersampled locations. We extend the type of covariate information u...
The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describ...
This comment reexamines Simard et al.’s work in [D. Simard, L. Nadeau, H. Kröger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity length...
The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image pro...
The famous connection between metric entropy and small deviation probabilities of Gaussian processes was discovered by Kuelbs and Li in [6] and completed by Li and Linde in [9]. The question whethe...
Let A = 􀀀 A(t)  t­0 be a subordinator. Given a compact set K  [0;1) we prove two-sided estimates for the covering numbers of the random set {A(t) : t 2 K} which depend on the Lapl...
P. Hitczenko, S.Kwapien, W.N.Li, G.Schechtman, T.Schlumprecht and J.Zinn stated the following conjecture. Let $mu$ be a symmetric $alpha$-stable measure on a separable Banach space and $B$ a centered ...
We show that there exist Lévy processes (X_t,t ≥ 0) and reals y>0 such that for small t, the probability P(X_t> y) has an expansion involving fractional powers or more general functions of t. This con...
We show that there exist Lévy processes (X_t,t ≥ 0) and reals y>0 such that for small t, the probability P(X_t> y) has an expansion involving fractional powers or more general functions of t. This con...

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