Regularity of the powers of an ideal

For a homogeneous ideal I of S = A[X_o,... ,X_n] we compare the Castelnuovo-Mumford regularities of the powers of I to the regularity reg I of I itself.     

Tunable size and spectral properties of fluorescent nanoGUMBOS in modified sodium deoxycholate hydrogels

Microstructures of sodium deoxycholate hydrogels were altered considerably in the presence of variable tris(hydroxymethyl)aminomethane (TRIS) concentrations. These observations were confirmed by use of X-ray diffraction, polarized optical microscopy, rheology, and differential scanning calorimetry measurements. Our studies reveal enhanced gel crystallinity and rigidity with increasing TRIS concentrations. The tunable hydrogel microstructures obtained under various conditions have been successfully utilized as templates to synthesize cyanine-based fluorescent nanoGUMBOS (nanoparticles from a group of uniform materials based on organic salts). A systematic variation in size (70-200 nm), with relatively low polydispersity and tunable spectral properties of [HMT][AOT] nanoGUMBOS, was achieved by use of these modified hydrogels. The gel microstructures are observed to direct the size as well as molecular self-assembly of the nanomaterials, thereby tuning their spectral properties. These modified hydrogels were also found to possess other interesting properties such as variable morphologies ranging from fibrous to spherulitic, variable degrees of crystallinity, rigidity, optical activity, and release profiles which can be exploited for a multitude of applications. Hence, this study demonstrates a novel method for modification of sodium deoxycholate hydrogels, their applications as templates for nanomaterials synthesis, as well as their potential applications in biotechnology and drug delivery.     

Tuning supported catalyst reactivity with dendrimer-templated Pt-Cu nanoparticles

The effects of particle composition on heterogeneous catalysis were studied using dendrimer-encapsulated nanoparticles (DENs) as precursors to supported Pt-Cu catalysts. Bimetallic Pt-Cu DENs with varying Pt/Cu ratios were prepared in an anaerobic aqueous solution and deposited onto a high-purity commercial alumina support. The dendrimer template was then thermally removed to yield supported nanoparticle catalysts, which were studied with toluene hydrogenation and CO oxidation catalysis as well as infrared spectroscopy of adsorbed CO. Incorporating Cu into Pt nanoparticles had opposite effects on the two test reactions. Cu acted as a mild promoter for CO oxidation catalysis, and the promoting effect was independent of the amount of Cu present. Conversely, Cu acted as a strong poison for toluene hydrogenation catalysis, and the normalized rate tracked inversely with Cu content. Infrared spectroscopy of the supported nanoparticles indicated that electronic effects (electron donation from Cu to Pt) were minimal for these materials. Consequently, the catalysis results are interpreted in terms of potential structural differences as a function of Cu incorporation and reaction conditions.     

The permutation action of finite symplectic groups of odd characteristic on their standard modules

We study the space of functions on a finite-dimensional vector space over a field of odd order as a module for a symplectic group. We construct a basis of this module with the following special properties. Each submodule generated by a single basis element under the symplectic group action is spanned as a vector space by a subset of the basis and has a unique maximal submodule. From these properties, the dimension and composition factors of the submodule generated by any subset of the basis can be determined. These results apply to incidence geometry of the symplectic polar space, yielding the symplectic analogue of Hamada's additive formula for the p-ranks of the incidence matrices between points and flats. A special case leads to a closed formula for the p-rank of the incidence matrix between the points and lines of the symplectic generalized quadrangle over a field of odd order. Together with earlier results on the 2-ranks, this result completes the determination of the p-ranks for these quadrangles.     

Optimization of air vehicles operations using mixed-integer linear programming

A scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. Furthermore, multiple tasks are to be successively performed on each target, that is, the targets must be classified, attacked, and verified as destroyed. The optimal, for example, minimum time, performance of these tasks requires cooperation among the vehicles such that critical timing constraints are satisfied, that is, a target must be classified before it can be attacked, and an air vehicle is sent to a target area to verify its destruction only after the target has been attacked. In this paper, the optimal task assignment/scheduling problem is posed as a mixed-integer linear program (MILP). The solution of the MILP assigns all tasks to the vehicles and performs the scheduling in an optimal manner, including staged departure times. Coupled tasks involving timing and task order constraints are automatically addressed. When the air vehicles have sufficient endurance, the existence of a solution is guaranteed.     

An improved 1D fiber dry spinning mass transfer model

A method of extending one-dimensional models of fiber dry spinning to take differences between surface and average mass concentrations into account is evaluated using an idealized model problem. Based on a closed form solution of the model problem, it is concluded that the method (which involves the introduction of a separate surface concentration variable and a corresponding additional equation) works well.     

Estimating biodegradative gene numbers at a JP-5 contaminated site using PCR

Applied Biochemistry and Biotechnology - We have utilized a most-probable-number polymerase chain reaction (MPN-PCR) procedure to estimate gene numbers and biodegradative potential at a jet fuel...