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.     

Uniform estimates for a variational problem with small parameters

Communicated by J. M. Ball     

Rearrangements of (0–1) matrices

Let ℬ(m) be the set of all then-square (0–1) matrices containingm ones andn ²−m zeros, 0<m<n ². The problem of finding the maximum ofs(A ²) over this set, wheres(A ²) is the sum of the entries ofA ²,A ∈ ℬ (m) is considered. This problem is solved in the particular casesm=n ² −k ² andm=k ²,k ²>(n ²/2). This paper forms part of a thesis in partial fulfillment of the requirements for the degree of Doctor of Science at the Technion-Israel Institute of Technology. The author wishes to thank Professor B. Schwarz and Dr. D. London for their help in the preparation of this paper.     

C-Programming: An outline

This paper presents the essentials of a method designed to solve optimization problems whose objective functions are of the form g(x)+ ψ(u(x)), where ψ is differentiable and either concave or convex. It is shown that solutions to such problems can be obtained through the solutions of the Lagrangian problem whose objective function is of the form g(x)+ λu(x).     

Determination of Economic Packaging Set-up Frequency of Jointly Replenished Items

This paper deals with the problem of determining the economic operating policy for inventory items which are manufactured jointly but packaged individually. The proposed new approach is very simple and efficient. An extensive simulation study is presented so that the results of several heuristics (based on a wide range of data, measuring the number of optimal solutions, average error and maximum error) can be compared.