Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Radio-frequency plasma cleaning for mitigation of high-power microwave-pulse shortening in a coaxial gyrotron

Results are reported demonstrating that radio-frequency (rf) plasma cleaning is an effective technique for mitigating microwave-pulse shortening (i.e., lengthening the pulse) in a multimegawatt, large-orbit, coaxial gyrotron. Cleaning plasmas were generated by 50 W of rf power at 13.56 MHz in nitrogen fill gas in the pressure range 15–25 mTorr. Improvements in the averaged microwave energy output of this high-power-microwave device ranged from 15% to 245% for different initial conditions and cleaning protocols. The mechanism for this improvement is believed to be rf plasma sputtering of excess water vapor from the cavity/waveguide and subsequent removal of the contaminant by cryogenic vacuum pumps. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71003/2/APPLAB-77-23-3725-1.pd

A biophysical model of cell adhesion mediated by immunoadhesin drugs and antibodies

A promising direction in drug development is to exploit the ability of natural killer cells to kill antibody-labeled target cells. Monoclonal antibodies and drugs designed to elicit this effect typically bind cell-surface epitopes that are overexpressed on target cells but also present on other cells. Thus it is important to understand adhesion of cells by antibodies and similar molecules. We present an equilibrium model of such adhesion, incorporating heterogeneity in target cell epitope density and epitope immobility. We compare with experiments on the adhesion of Jurkat T cells to bilayers containing the relevant natural killer cell receptor, with adhesion mediated by the drug alefacept. We show that a model in which all target cell epitopes are mobile and available is inconsistent with the data, suggesting that more complex mechanisms are at work. We hypothesize that the immobile epitope fraction may change with cell adhesion, and we find that such a model is more consistent with the data. We also quantitatively describe the parameter space in which binding occurs. Our results point toward mechanisms relating epitope immobility to cell adhesion and offer insight into the activity of an important class of drugs.Comment: 13 pages, 5 figure

Color television system for a manned space base Progress report

Color television system for manned space statio

A Scorecard for Indexed Government Debt

Within the last five years, Canada, Sweden and New Zealand have joined the ranks of the United Kingdom and other countries in issuing government bonds that are indexed to inflation. Some observers of the experience in these countries have argued that the United States should follow suit. This paper provides an overview of the issues surrounding debt indexation, and it tries to answer three empirical questions about indexed debt. First, how different would the returns on indexed bonds be from the returns on existing US debt instruments? Second, how would indexed bonds affect the government's average financing costs? Third, how might the Federal Reserve be able to use the information contained in the prices of indexed bonds to help formulate monetary policy? The paper concludes with a more speculative discussion of the possible consequences of increased use of indexed debt contracts by the private sector.

Homoleptic [ONO]2Ti(IV) type complexes of amino-acid-tethered phenolato, Schiff-base ligands: Synthesis, characterization, time-resolved fluorescence spectroscopy, and cytotoxicity against ovarian and colon cancer cells

Six homoleptic Ti(IV) compounds of dianionic tridentate Schiff base ligands were synthesized from chiral amino acids, 2-hydroxybenzaldehyde and Ti(OiPr)4. The compounds were spectroscopically characterized and the molecular geometries were established by X-ray crystallography. The ligands coordinated the titanium via carboxylate-O-, imine-N-, and phenoxide-O atoms. Two isomers were identified; each based on a trans-N2O4 donor set, but one with trans carboxylate-O atoms and another with each carboxylate-O atom trans to a phenoxide-O atom. Photophysical profiles exhibited faster excited-state relaxation in the solid phase than in solution. Marked cytotoxicities were recorded toward human ovarian A2780 and colon HT-29 cancer cells with IC50 values ranging between 23±2 and 103±3 µM. Comparative hydrolytic stability studies by NMR in 10% D2O solutions provided t1/2 values of up to 15±2 h, with little correlation to cytotoxicity implying a role of hydrolysis products in the reactivity and identifying steric bulk as a contributor to stability and solubility

New Concepts in Median Nail Dystrophy, Onychomycosis, and Hand, Foot, and Mouth Disease Nail Pathology

Nails are underutilized as diagnostic tools, despite being involved in many dermatologic conditions. This paper explores new concepts in the treatment of median nail dystrophy (MND), onychomycosis, and the nail pathology of hand, foot, and mouth disease (HFMD). A Pubmed database literature search was conducted for MND treatment, onychomycosis treatment, and HFMD nail pathology. Only papers published after January 2008 were reviewed. The results showed that 0.1% tacrolimus ointment can be an effective treatment for MND. Early studies on laser therapy indicate that it is a safe and efficacious treatment option for onychomycosis, compared to conventional oral antifungal agents. Vicks VapoRub (The Proctor & Gamble Company, Cincinnati, OH) is effective against onychomycosis and is a reasonable option in patients who choose to forgo conventional treatments. Lastly, there is evidence to support a correlation between HFMD and onychomadesis