where E ranges among all sets of finite perimeter satisfying the constraint LN (E) = const., νE is the generalized inner normal to E and ∂∗E is the reduced boundary of E (see the definitions in Section 2). For an anisotropic function Γ, one of the first attempts to solve this problem is contained in a paper by G.Wulff [22] dating back to 1901. However, it was only in 1944 that A.Dinghas [9] pro...

In this note we sketch the proofs of two results in combinatorial set theory. The common theme of the results is singular cardinal combinatorics: they involve the interaction between forcing, large cardinals, PCF theory and versions of Jensen’s weak square principle. 1. Changing cofinality Our first result involves an old question about changes of cofinality. Suppose that V,W are inner models o...

The problem of packing boxes into a large box is often a part of a larger problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution centers and stores, such that the furniture fits inside. Such problems are often formulated and sometimes solved using generalpurpose integer programming solv...

The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M . For string compression, straight-line programs, i.e., contextfree grammars that generate a single string, are used in this paper. It is shown that the compressed word problem for a free inverse monoid of finite rank at least two is comp...

The space now known as complete Erdős space Ec was introduced by Paul Erdős in 1940 as the closed subspace of the Hilbert space l2 consisting of all vectors such that every coordinate is in the convergent sequence {0} ∪ {1/n : n ∈ N}. In a solution to a problem posed by Lex G. Oversteegen we present simple and useful topological characterizations of Ec. As an application we determine the class ...

The characteristic photon energy for Gamma Ray Bursts, Epeak, has a remarkably narrow distribution for bursts of similar peak flux, with values between 150 and 600 keV for most faint bursts. This result is surprising within the framework of internal shock models, since spectral shifts associated with the jet’s blue shift (by a Lorentz factor of Γ) and the cosmological red shift (by a factor of ...

The PTB domain of mouse dok1 fusion protein has been overexpressed in Escherichia coli and crystallized in a form suitable for X-ray crystallographic study. Crystals have been obtained using the vapour-diffusion method and belong to space group P2(1)2(1)2(1). X-ray diffraction data were collected in-house to 2.5 A resolution. A selenomethionine (SeMet) dok1 PTB fusion-protein derivative was exp...

(1) It is shown that if c is real-valued measurable then the Maharam type of (c,P(c), σ) is 2. This answers a question of D. Fremlin [Fr,(P2f)]. (2) A different construction of a model with a real-valued measurable cardinal is given from that of R. Solovay [So]. This answers a question of D. Fremlin [Fr,(P1)]. (3) The forcing with a κ-complete ideal over a set X , |X | ≥ κ cannot be isomorphic ...

As the power of scientific computing continues to grow, detailed models for complex chemical-transport phenomena play a more significant role in the design process of advanced energy conversion devices (Hwang et al. 2008). As a result, there have been substantial research efforts devoted to the construction and further development of detailed chemical models for conventional and alternative fue...

We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for preprocessing via simple and/or local reduction rules. We find kernelizations for d-hitting set(k), d-set packing(k), edge dominating set(k) and a number of hitting and...