Wave fans are special

It is shown that self-similar BV solutions of genuinely nonlinear strictly hyperbolic systems of conservation laws are special functions of bounded variation, with vanishing Cantor part.     

ANNOUNCEMENT

A special issue of Acta Mathematica Scientia,to be published in 2011,will be dedicated to the 85th birthday of Peter D.Lax,who is one of the most prominent     

Lower bounds on the spectra of symmetric matrices with nonnegative entries

If we normalize a symmetric n × n matrix with nonnegative entriesso that its largest entry is 1, then its spectrum is bounded below by $\text{?n}\text{2}$. The lower bound is achieved in all even dimensions for (and only for) adjacency matrices of complete bipartite graphs with equal parts.     

Cooperative effects in the two atom resonance fluorescence spectrum

We consider the resonance fluorescence spectrum of two similar interacting atoms in the limit of high photon densities. The excitation spectrum of the symmetric modes contains two sidebands in addition to the usual three peaks which are analogous to those of the isolated atom. These two new sidebands are due entirely to the cooperative behaviour of the two atoms and vanish when the atoms are far apart. The energy shifts and spectral widths for these two sidebands are two and five times larger than those for the isolated atom respectively. The probability of occurrence of these sidebands depends on the parameters V_AB/Ω and γ²₀/Ω², where V_AB is the dipole-dipole interaction energy, γ₀ is the spontaneous emission probability and Ω is the Rabi frequency. The asymmetric broadening of both sidebands depends on the parameter γ₀/Ω. The possibility to measure the dipole-dipole energy through the observation of these sidebands is discussed.     

Entropy rigidity for finite volume strictly convex projective manifolds

Geometriae Dedicata - We prove entropy rigidity for finite volume strictly convex projective manifolds in dimensions $$\ge 3$$ , generalizing the work of [1] to the finite volume setting. The...     

Miconazole induces fungistasis and increases killing of Candida albicans subjected to photodynamic therapy

Cutaneous and mucocutaneous Candida infections are considered to be important targets for antimicrobial photodynamic therapy (PDT). Clinical application of antimicrobial PDT will require strategies that enhance microbial killing while minimizing damage to host tissue. Increasing the sensitivity of infectious agents to PDT will help achieve this goal. Our previous studies demonstrated that raising the level of oxidative stress in Candida by interfering with fungal respiration increased the efficiency of PDT. Therefore, we sought to identify compounds in clinical use that would augment the oxidative stress caused by PDT by contributing to reactive oxygen species (ROS) formation themselves. Based on the ability of the antifungal miconazole to induce ROS in Candida, we tested several azole antifungals for their ability to augment PDT in vitro. Although miconazole and ketoconazole both stimulated ROS production in Candida albicans, only miconazole enhanced the killing of C. albicans and induced prolonged fungistasis in organisms that survived PDT using the porphyrin TMP-1363 and the phenothiazine methylene blue as photosensitizers. The data suggest that miconazole could be used to increase the efficacy of PDT against C. albicans, and its mechanism of action is likely to be multifactorial.     

Lattice-theoretic properties of algebras of logic

In the theory of lattice-ordered groups, there are interesting examples of properties — such as projectability — that are defined in terms of the overall structure of the lattice-ordered group, but are entirely determined by the underlying lattice structure. In this paper, we explore the extent to which projectability is a lattice-theoretic property for more general classes of algebras of logic. For a class of integral residuated lattices that includes Heyting algebras and semi-linear residuated lattices, we prove that a member of such is projectable iff the order dual of each subinterval [a,1]$[a,1]$ is a Stone lattice. We also show that an integral GMV algebra is projectable iff it can be endowed with a positive Gödel implication. In particular, a ΨMV or an MV algebra is projectable iff it can be endowed with a Gödel implication. Moreover, those projectable involutive residuated lattices that admit a Gödel implication are investigated as a variety in the expanded signature. We establish that this variety is generated by its totally ordered members and is a discriminator variety.     

Groupable lattices

A lattice is called groupable provided it can be endowed with the structure of an l-group (lattice ordered group). The primary objective of this paper is to introduce an order theoretic property of groupable lattices which implies that all associated l-groups are subdirect products of totally ordered groups. This is an analog to Iwasawa's well-known result which asserts that a conditionally complete l-group is abelian. A secondary objective is to outline a general method for identifying classes of l-groups determined by order theoretic properties.     

Global optimization of multi-parametric MILP problems

In this paper, we present a novel global optimisation approach for the general solution of multi-parametric mixed integer linear programs (mp-MILPs). We describe an optimisation procedure which iterates between a (master) mixed integer nonlinear program and a (slave) multi-parametric program. Moreover, we explain how to overcome the presence of bilinearities, responsible for the non-convexity of the multi-parametric program, in two classes of mp-MILPs, with (i) varying parameters in the objective function and (ii) simultaneous presence of varying parameters in the objective function and the right-hand side of the constraints. Examples are provided to illustrate the solution steps.