here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

We provide a simple algorithmic argument to “explain” the concentration of measure phenomenon observed in the sum of independent random variables. Roughly speaking, we observe that without concentration of measure it would be possible to predict the outcome of a coin toss with probability greater than 1/2. We use this idea to derive an alternative proof of a Chernoff-Hoeffding bound for large d...

This is a correction to the author’s article [Multiscale Model. Simul., 10 (2012), pp. 383–417].

We study the Laplacian in L 2 (R 3) perturbed on an infinite curve Γ by a δ interaction defined through boundary conditions which relate the corresponding generalized boundary values. We show that if Γ is smooth and not a straight line but it is asymptotically straight in a suitable sense, and if the interaction does not vary along the curve, the perturbed operator has at least one isolated eig...

The Chernoff bounds provide very accurate information concerning the tail probabilities of most distrbhutions. in this paper we describe some relevant properties of these bounds.