Conical Ricci-flat nearly para-Kähler manifolds

In this paper, we classify conical Ricci-flat nearly para-Kähler manifolds having isotropic Nijenhuis tensor. More precisely, we give a bijective correspondence between this class of nearly para-Kähler manifolds and local cones $M_1 \times (a,b)$ over para-Sasaki-Einstein manifolds $(M_1,g_1,T)$ carrying a parallel 3-form with isotropic support. Moreover, we show that the cone over a para-Sasaki-Einstein five-manifold $(M_1,g_1,T)$ admits a family of parallel 3-forms with isotropic support. As an application our result yields first examples of Ricci-flat (non-flat) nearly para-Kähler structures.     

Local Rings of Embedding Codepth 3. Examples

A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a differential graded algebra structure, based on which one can classify local rings of embedding codepth 3. We give examples of algebra structures that have been conjectured not to occur.     

Negative specific heat in a quasi-2D vortex system

Negative specific heat is a dramatic phenomenon where processes decrease in temperature when adding energy. It has been observed in gravo-thermal collapse of globular clusters. We now report finding this phenomenon in bundles of nearly parallel, periodic, single-sign generalized vortex filaments in the electron magnetohydrodynamic (EMH) model for the unbounded plane under strong magnetic confinement. We derive the specific heat using a steepest descent method and a mean field property. Our derivations show that as temperature increases, the overall size of the system increases exponentially and the energy drops. The implication of negative specific heat is a runaway reaction, resulting in a collapsing inner core surrounded by an expanding halo of filaments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weighted proximity search

Journal of Heuristics - Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of the problem at hand is replaced by...     

Hydrogen-bond topology and the ice VII/VIII and ice Ih/XI proton-ordering phase transitions

The existence of an ice Ih/XI proton-ordering transition to a low-temperature ferroelectric phase has sparked considerable debate in the literature. Electronic density functional theory calculations, extended using graph invariants, confirm that a transition to a low-temperature ferroelectric phase should occur. The predicted transition at 98 K is in qualitative agreement with the observed transition at 72 K, and the low-temperature phase is the ferroelectric phase determined in diffraction experiments. The theoretical methods used to predict the phase transition are validated by comparing their prediction to the well-characterized ice VII/VIII proton-ordering transition.     

Assessing the polarization of a quantum field from stokes fluctuations

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.     

Generalized Latin rectangles I: Construction and decomposition

A (p, q, x)-latin rectangle is a rectangular matrix with x symbols in each cell such that each symbol occurs at most p times in each row and at most q times in each column. We exploit the close correspondence between (p, q, x)-latin rectangles and equitable edge-colourings of certain graphs. This paper contains results on existence and various forms of decomposition of such rectangles. In a sequel paper embedding is considered.     

A jump operator on honest subrecursive degrees

It is well known that the structure of honest elementary degrees is a lattice with rather strong density properties. Let and denote respectively the join and the meet of the degrees and . This paper introduces a jump operator () on the honest elementary degrees and defines canonical degrees and low and high degrees analogous to the corresponding concepts for the Turing degrees. Among others, the following results about the structure of the honest elementary degrees are shown: There exist low degrees, and there exist degrees which are neither low nor high. Every degree above is the jump of some degree, moreover, for every degree above there exist degrees such that . We have and . The jump operator is of course monotonic, i.e. . We prove that every situation compatible with is realized in the structure, e.g. we have incomparable degrees such that and incomparable degrees such that etcetera. We are able to prove all these results without the traditional recursion theoretic constructions. Our proof method relies on the fact that the growth of the functions in a degree is bounded. This technique also yields a very simple proof of an old result, namely that the structure is a lattice. Received October 4, 1995