Let X be a Banach space and Z a nonempty closed subset of X. Let J :Z → R be an upper semicontinuous function bounded from above. This paper is concerned with the perturbed optimization problem supz∈Z{J (z)+ ‖x − z‖}, which is denoted by (x, J )-sup. We shall prove in the present paper that if Z is a closed boundedly relatively weakly compact nonempty subset, then the set of all x ∈X for which ...

We calculate the rate of production ofW+Υ and Z0+Υ at the Tevatron. We find the cross sections at a center-of-mass energy of 1.8 TeV to be roughly 450 pb for W+Υ and 150 pb for Z0+Υ. The dominant production mechanism involves the binding of a color-octet bb̄ pair into a P-wave bottomonium state which subsequently decays into Υ. The purely leptonic decay modes of Υ, W, and Z0 provide signatures w...

In this paper we derive quantitative uniqueness estimates at infinity for solutions to an elliptic equation with unbounded drift in the plane. More precisely, let u be a real solution to ∆u + W · ∇u = 0 in R2, where W is real vector and ‖W‖Lp(R2) ≤ K for 2 ≤ p <∞. Assume that ‖u‖L∞(R2) ≤ C0 and satisfies certain a priori assumption at 0. Then u satisfies the following asymptotic estimates at R ...

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary point z0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away from z0 cannot vanish to infinite order at z0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the...

There is a canonical homomorphism ψ : π1(bdyX)→ π∞ 1 (X) from the fundamental group of the visual boundary, here denoted by bdy X, of any non-positively curved geodesic space X into its fundamental group at infinity. In this setting, the latter group coincides with the first shape homotopy group of the visual boundary: π∞ 1 (X) ≡ π̌1(bdy X). The induced homomorphism φ : π1(bdy X)→ π̌1(bdy X) prov...

We say that a simple graph G is Seidel integral if its spectrum consists entirely of integers. If ?Ka,a ? ?Kb,b integral, we show it belongs the class graphs [kt/? x0 + mt/?z]Ka,a y0 a/?z]nKb,b, where (i) = (t+?n)k+?m and b ?m; (ii) t, k, ?,m, n N such (m, n) 1, (n, t) 1 (?, 1; (iii) (a,mt) | kt; (iv) (x0, y0) particular solution linear Diophantine equation ax (mt)y (v) z z0 least integer (kt/?...

The interaction force gradient between a micron-size polystyrene sphere and an atomically flat highly oriented pyrolytic graphite substrate has been analyzed as a function of surface-to-surface separation distance z0 using an oscillating cantilever technique. The interaction force gradient was found to have two contributions. For z0>30 nm, an electrostatic force due to charges trapped on the po...

It is shown that, for solid caps D of heat balls in Rd+1 with center z0 = (0, 0), there exist Borel measurable functions w on D such that inf w(D) > 0 and ∫ v(z)w(z) dz ≤ v(z0), for every supertemperature v on a neighborhood of D. This disproves a conjecture by N. Suzuki and N.A. Watson. On the other hand, it turns out that there is no such volume mean density, if the bounded domain D in Rd × (...