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.     

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.     

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...     

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.     

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.     

High-Solids,Solvent-Free Modification of Engineered Polysaccharides

The nature-identical engineered polysaccharide α-(1,3) glucan, produced by the enzymatic polymerization of sucrose, was chemically modified by acylation with succinic anhydride. This modification reaction was initially performed at the micro scale in a TGA reactor to access a range of reaction conditions and to study the mechanism of the reaction. Subsequently, the best performing conditions were reproduced at the larger laboratory scale. The reaction products were characterized via coupled TGA/DSC analysis, FT-IR spectroscopy, solution viscosity and pH determination. The acylation path resulted in partially modifying the polysaccharide by altering its behavior in terms of thermal properties and solubility. The acylation in a solvent-free approach was found promising for the development of novel, potentially melt-processable and fully bio-based and biodegradable ester compounds.     

Droplet spindown in a high-temperature gas environment

The spindown and heating of a spherical droplet in an initially undisturbed infinite fluid is investigated by means of a numerical model based on finite-difference discretization techniques. The nonevaporating droplet enters the hot gas while rotating about a diameter and has no translational motion with respect to the suspending medium. Special attention is given to the transient secondary (nonrotational) motion developed as a result of shear interaction between the two phases. The results indicate that for droplet sizes and rotation frequencies representative of droplet combustion applications; i.e., Reynolds ∼ O(0.1), the secondary motion in both phases remains weak and heat transport is conduction-dominated. On the other hand, the secondary motion is strengthened with increased values of the rotational Reynolds number. The characteristic time for droplet spindown is found to be proportional to the square of the droplet radius. The results also show that the rotational deceleration time is of the same order of magnitude with the translational response time of the droplet. Finally, the thermocapillary stress effects on fluid dynamics and heat transfer are investigated in this flow configuration.     

Bounds on linear PDEs via semidefinite optimization

Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this paper a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on linear functionals defined on solutions of linear partial differential equations. We apply the proposed method to examples of PDEs in one and two dimensions, with very encouraging results. We pay particular attention to a PDE with oblique derivative conditions, commonly arising in queueing theory. We also provide computational evidence that the semidefinite constraints are critically important in improving the quality of the bounds, that is, without them the bounds are weak. Research supported by the SMA-MI Talliance. Research partially supported by the SMA-MIT alliance and an NSF predoctoral fellowship.     

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.