If Ω is any compact Lipschitz domain, possibly in a Riemannian manifold, with boundary Γ = ∂Ω, the Dirichlet-to-Neumann operator Dλ is defined on L2(Γ) for any real λ. We prove a close relationship between the eigenvalues of Dλ and those of the Robin Laplacian ∆μ, i.e. the Laplacian with Robin boundary conditions ∂νu = μu. This is used to give another proof of the Friedlander inequalities betwe...

Let q denote a large prime number, a be any integer. Let N(q, a) denote the smallest positive integer n for which φ(n) ≡ a (mod q). The number N(q, a) exists. Indeed, if a+1 ≡ 0 (mod q) then one can take n = q. Otherwise, one can take n to be a prime from the arithmetical progression a + 1 (mod q). The problem of upper bound estimates for N(q, a) has been a subject of study of the work of Fried...

The morbidity and mortality of anaesthesia and surgery are increased by cardiac diseases. It is essential, therefore, to recognize the presence of cardiovascular diseases and to assess their severity in order to prevent serious complication during anaesthesia and the period after operation. Relatively silent cardiac or vascular diseases are often first diagnosed during the preoperative visit (K...

In this paper, we present a new method for minimizing a convex quadratic function of many variables with box constraints. The new algorithm is a modiication of a method introduced recently by Friedlander and Mart nez (SIAM J. on Optimization, febru-ary 1994). Following the lines of Mor e and Toraldo (SIAM J. on Optimization 1, pp. 93-113), it combines an eecient unconstrained method with gradie...

s=1/2 where E(z, s) is the Eisenstein series for SL2(Z). In general one tries to deduce good estimates for these sums assuming the parameters a, b, h are of considerable size. The additive divisor problem has an extensive history and we refer the reader to [1] for a short introduction. Let us just mention that in the special case a = b = 1 one can derive very sharp results by employing the spec...

This issue of SIAG/OPT Views-and-News is dedicated to the 2011 SIAM Conference on Optimization. Claudia Sagastizábal has written a beautiful and elegant survey of nonsmooth optimization showing how traditional methods can be cleverly improved by exploiting structure beyond the black box. Don’t miss her plenary presentation on Wednesday at 1pm! Other highlights of OP11 include the SIAG/OPT busin...

Let G be a simple, simply connected algebraic group defined and split over the prime field F p > 3. Let F be a finite dimensional rational G-module. As shown in [1] , for d suitably large, the Eilenberg-Mac Lane cohomology groups H*(G(Fpd), V) achieve a stable value H*en(G, V)9 the so-called generic cohomology of V. This generic cohomology can in turn be determined from the rational cohomology ...