Analysis of a Polynomial System Arising in the Design of an Optical Lattice Filter Useful in Channelization

In this work, we consider design questions for an active optical lattice filter, which is being manufactured at the University of Texas at Dallas, and which has proven to be useful in the signal processing task of RF channelization. The filter can be described by a linear, discrete time state space model. The controlling agents, the gains, are embedded in the matrices intervening in this state space model. Consequently, techniques from linear feedback control theory do not apply. We concentrate on the question of finding real valued gains so that the A matrix of the state space model has a prescribed characteristic polynomial. We find that three of the coefficients can be arbitrarily picked, but that the remaining are constrained by these and the other system parameters. Our techniques use methods from constructive algebraic geometry.     

The optimisation of facile substrates for surface enhanced Raman scattering through galvanic replacement of silver onto copper

A fast and cost-effective approach for the synthesis of substrates used in surface enhanced Raman scattering (SERS) has been developed using galvanic displacement. Deposition of silver onto commercially available Cu foil has resulted in the formation of multiple hierarchical structures, whose morphology show dependence on deposition time and temperature. Analysis of the surface structure by scanning electron microscopy revealed that the more complex silver structures correlated well with increased deposition time and temperature. Using Rhodamine 6G (R6G) as a model Raman probe it was also possible to relate the substrate morphology directly with subsequent SERS intensity from the R6G analyte as well as the reproducibility across a total of 15 replicate Raman maps (20 × 20 pixels) consisting of 400 spectra at a R6G concentration of 10(-4) M. The substrate with the highest reproducibility was then used to explore the limit of detection and this compared very favourably with colloidal-based SERS assessments of the same analyte.     

Equiangular tight frames and fourth root seidel matrices

In this paper we construct complex equiangular tight frames (ETFs). In particular, we study the grammian associated with an ETF whose off-diagonal entries consist entirely of fourth roots of unity. These ETFs are classified, and we also provide some computational techniques which give rise to previously undiscovered ETFs.     

A Partnership Approach to Improving Student Attitudes About Sharks and Scientists

This article describes the methods and impact of a student–teacher–scientist research partnership on student attitudes. The partnership objective was to teach students about the diverse roles of sharks in the marine environment while personally connecting students with scientific study. Students (N = 229) participated in lessons about shark biology and helped the partnering scientist design experimental protocols and analyze data. A self‐selected subset of students also volunteered (n = 82) for a field component working with live hammerhead sharks (Sphyrna lewinii). Student surveys before and after the partnership suggested that negative attitudes about sharks are due largely to lack of exposure, and direct attention to students' stereotypes about sharks resulted in significant attitude improvement. Change in students' attitudes toward scientists, however, was minimal. Students' negative views of scientists did decline significantly, but their overall views of scientists were relatively positive to begin with. Also of interest was the students' unremitting association of scientists with specialized equipment and the students' lack of personal connection to scientific ways of examining the world, suggesting that partnerships may be more effective at personally connecting students with scientific process if they explicitly incorporate activities designed to improve students' view of themselves as scientists.     

Cell Uptake and Trafficking Behavior of Non‐covalent,Coiled‐coil Based Polymer–Drug Conjugates

This paper reports on the cell uptake and trafficking properties of a series of non‐covalent polymer–drug conjugates. These nanomedicines are composed of a poly(N‐(2‐hydroxypropyl)methacrylamide) backbone functionalized with multiple copies of a drug. The drug moieties are attached to the polymer via a non‐covalent, so called coiled coil motif, which is formed by heterodimerization of two complementary peptide strands, one of which is attached to the polymer carrier and the other to the drug. Cytotoxicity and FACS experiments, which were carried out with model anticancer drug or fluorophore conjugates, provided insight into the cell uptake and trafficking behavior of these conjugates.

     

Hexamethylsilirane : I. Preparation,characterization and thermal decomposition

Hexamethylsilirane has been prepared by the action of magnesium on dimethyl-bis(α-bromoisopropyl)silane in tetrahydrofuran (THF) solution. It was found to be highly reactive toward atmospheric oxygen and moisture and to decompose when heated in solution at 60–75°C. Its decomposition results in the extrusion of dimethylsilylene which may add to the tetramethylethylene produced in the decomposition to regenerate the silirane, insert into the reactive SiC₂ ring of the silirane to give octamethyl-1,2-disilacyclobutane or oligomerize to give (Me₂Si)_n oils.Dimethyldiisopropyl-, tetraisopropyl- and tert-butyltriisopropylsilane were prepared by catalytic hydrogenation of the corresponding isopropenylsilanes. Bromination of dimethyldiisopropylsilane at 65°C resulted in exclusive formation of dimethyl-bis(α-bromoisopropyl)silane.     

Interpreting Negative Results in an Angle Maximization Problem

The correct interpretation of positive and negative results in a situation involving mathematical modeling poses problems for some students. This article presents a situation in which differential calculus is used with inverse trigonometric tangentfunctions to maximize an angle measure. A negative distance measure ultimately results, thus requiring a reconsideration of assumptions inherent in the initial figure.