So what possessed CPU designers to cause them to inflict memory barriers on poor unsuspecting SMP software designers? In short, because reordering memory references allows much better performance, and so memory barriers are needed to force ordering in things like synchronization primitives whose correct operation depends on ordered memory references. Getting a more detailed answer to this quest...

In a previous paper we have considered the functional V (u) = 1 2 ∫ RN | grad u(x)| dx+ ∫ RN F (u(x)) dx subject to ∫ RN G(u(x)) dx = λ > 0 , where u(x) = (u1(x), . . . , uK(x)) belongs to H 1 K(R ) = H(R ) × · · · × H(R) (K times) and | grad u(x)| means ∑K i=1 | gradui(x)|. We have shown that, under some technical assumptions and except for a translation in the space variable x, any global min...

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, Fn(X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(Fn(X)). We co...

Let D be a symmetric design admitting a null polarity such that either all singular lines, or all nonsingular lines, have size (v − λ)/(k − λ); assume that this number is greater than λ in the case of singular lines. Then D is either a projective space or an orthogonal symmetric design. © 2003 Elsevier Ltd. All rights reserved. The Dembowski–Wagner Theorem [3] characterizes projective spaces as...

We consider a skew-symmetric n -ary bracket on the polynomial algebra K [ x 1 , … + ] ( ≥ 2 ) over field of characteristic zero defined by { } = Jac C where is fixed element and Jacobian. If then this Poisson if 3 it an -Lie-Poisson . describe center corresponding show that quotient / − λ ideal generated 0 ≠ ∈ simple central homogeneous not proper power any nonzero polynomial. This construction...

The X = M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac–Moody algebra. In this paper we prove the X = M conjecture for tensor products of Kirillov–Reshetikhin crystals B1,s associated to symmetric powers for all nonexcep...

A recent conjecture on two-dimensional foams suggested that for fixed topology with given bubble areas there is a unique state of stable equilibrium. We present counter-examples, consisting of a ring of bubbles around a central one, which refute this conjecture. The discussion centres on a novel form of instability which causes symmetric clusters to become distorted. The stability of these bubb...

The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in d = 4 space-time dimensions. Comparisons with previous partial results, as well as the fake supergravity (first order) formalism and an analysis of t...

Λ:λրΛ(cα(b) + u)(cα(b) + v)κα(λ,Λ)φ(Λ) = (nα + uv) φ(λ), where cα(b) is the α-content of a new box b = Λ \ λ. If α = 1, this identity implies the existence of an interesting family of positive definite central functions on the infinite symmetric group. The approach is based on the interpretation of a Young diagram as a pair of interlacing sequences, so that analytic techniques may be used to so...