Maximal solutions of semilinear elliptic equations with locally integrable forcing term

We study the existence of a maximal solution of −Δu+g(u)=f(x) in a domain Ω ∈ ℝ ^N with compact boundary, assuming thatf ∈ (L _loc ¹ (Ω))₊ and thatg is nondecreasing,g(0)≥0 andg satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classicalC _1,2 Wiener criterion, then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition, we discuss the question of uniqueness of large solutions. This research was partially supported by an EC Grant through the RTN Program “Front-Singularities”, HPRN-CT-2002-00274.     

Two dimorphs of 5‐methyl­sulfanyl‐1H‐tetrazole

5‐Methyl­sulfanyl‐1H‐tetrazole, C₂H₄N₄S, crystallizes in dimor­phic forms; the α‐form crystallizes at room temperature in the monoclinic crystal system, space group P2₁/m, and the β‐form crystallizes by sublimation at 423 K in the orthorhombic crystal system, space group Pbcm. In both forms, the mol­ecules occupy crystallographic mirror planes and are connected to one another via N—H⋯N hydrogen bonds, the amino H atoms being disordered. The two forms differ from one another in their packing; there are polar layers in the α‐form and non‐polar layers in the β‐form.     

Hilbert-Carleman and regularized determinants for linear operators

A general theory of regularized and Hilbert-Carleman determinants in normed algebras of operators acting in Banach spaces is proposed. In this approach regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators. We characterize the algebras for which such extensions exist, describe the main properties of the extended determinants, obtain Cramer's rule and the formulas for the resolvent which are expressed via the extended tracestr(A ^k ) of iterations and regularized determinants.This paper is a continuation of the paper [GGKr].     

Uniform estimates for a variational problem with small parameters

Communicated by J. M. Ball     

Electron spin resonance spectrum of the diphenylcyclobutene anion radical

The anion radical of 1,2-diphenylcyclobutene was studied by electron spin resonance. The hyperfine splittings were found to be 0·47 and 0·74 G for the meta-positions, 2·23 and 2·69 G for the ortho-positions and 4·21 G for the para-positions of the phenyl rings. The methylene proton splittings were 4·27 G, which would imply that the value of Q is 27 G, much lower than that of other cyclobutene anions. It was also estimated that the angle between the axis of the p-orbitals of the ethylene group and that of the phenyl group is about 30°, in agreement with that found for the tetraphenylethylene anion.     

On the space-filling enneahedra

A space-filling polyhedron is one whose replications can be packed to fill three-space completely. The space-filling polyhedra of four to eight faces have been previously reported. The search is here extended to the convex space-fillers of nine faces. The number of types is found to be at least 40.     

Can projectiles traversing solids bind electrons at all velocities?

PAC measurements on the 4.43 MeV ¹²C(2⁺) state on recoil in magnetized iron at velocities υ_ion = 0.058c, 0.071c yield integral nuclear precession angles of Φ = ?0.18 (30), +0.17 (39) mrad respectively. Evidently, the high electron-spin-polarization transfer to the innermost carbon orbits implied by a previous measurement (υ_ion = 0.03c, Φ = +0.85 (14) mrad) is suppressed at higher ion velocities.