L2 regularity of measurable solutions of a finite-difference equation of the circle

We show that if $\varphi$ is a lacunary Fourier series and the equation $\psi (x) -\psi (x + \alpha) = \varphi(x), x \bmod 1$ has a measurable solution $\varphi$, then in fact the equation has a solution in L2. This work of Michel Herman (1942-2000) appeared only as a preprint of the Mathematics Institute, University of Warwick, dated May 1976. It was turned into TEX format by Claire Desescures. Minor editorial work was done by Albert Fathi

The effect of the near earth micrometeoroid environment on a highly reflective mirror surface

A resurgence of interest in placing large solar concentrator solar dynamic systems in space for power generation has brought up again a concern for maintaining the integrity of the optical properties of highly specular reflecting surfaces in the near earth space environment. One of the environmental hazards needing evaluation is the micrometeoroid environment. It has been shown that highly reflective polished metals and thin film coatings degrade when exposed to simulated micrometeoroids in the lab. At NASA-Lewis, a shock tube was used to simulate the phenomenon of micrometeoroid impact by accelerating micron sized particles to hypervelocities. Any changes in the optical properties of surfaces exposed to this impact were then evaluated. The degradation of optical properties of polished metals and thin metallic films after exposure to simulated micrometeoroids was determined as a function of impacting kinetic energy area of the particles. A calibrated sensor was developed to not only detect the micrometeoroid environment, but also to evaluate the degradation of the optical properties of thin aluminum films in space. Results of the simulation are presented and discussed

Airflow sensing system

Disclosed is an airflow sensing system for determining the type of airflow flowing over a flight surface. A hot film sensor is driven by a constant voltage feedback circuit that maintains the voltage across the sensor at a predetermined level. A signal processing circuit receives an output signal of the feedback circuit and determines whether the output signal is indicative of laminar, transitional or turbulent airflow. Transitional airflow is distinguished from turbulent airflow by a signal having significant energy in a low-frequency passband from 50-80 Hz. The signal processing circuit drives a three-color LED display to provide a visual indication of the type of airflow being sensed

N-Methylmesoporphyrin IX Fluorescence As A Reporter Of Strand Orientation In Guanine Quadruplexes

Guanine quadruplexes (GQ) are four-stranded DNA structures formed by guanine-rich DNA sequences. The formation of GQs inhibits cancer cell growth, although the detection of GQs invivo has proven difficult, in part because of their structural diversity. The development of GQ-selective fluorescent reporters would enhance our ability to quantify the number and location of GQs, ultimately advancing biological studies of quadruplex relevance and function. N-methylmesoporphyrin IX (NMM) interacts selectively with parallel-stranded GQs; in addition, its fluorescence is sensitive to the presence of DNA, making this ligand a possible candidate for a quadruplex probe. In the present study, we investigated the effect of DNA secondary structure on NMM fluorescence. We found that NMM fluorescence increases by about 60-fold in the presence of parallel-stranded GQs and by about 40-fold in the presence of hybrid GQs. Antiparallel GQs lead to lower than 10-fold increases in NMM fluorescence. Single-stranded DNA, duplex, or i-motif, induce no change in NMM fluorescence. We conclude that NMM shows promise as a turn-on\u27 fluorescent probe for detecting quadruplex structures, as well as for differentiating them on the basis of strand orientation

Interactions of Cbl with Grb2 and phosphatidylinositol 3\u27-kinase in activated Jurkat cells

T-cell receptor (TCR) cross-linking increases tyrosine phosphorylation of multiple proteins, only a few of which have been identified. One of the most rapidly tyrosine-phosphorylated polypeptides is the 120-kDa product of the proto-oncogene c-cbl, a cytosolic and cytoskeletal protein containing multiple proline-rich motifs that are potential binding sites for proteins containing Src homology 3 (SH3) domains. We report here that in cultured Jurkat T cells, Cbl is coprecipitated with antibody against the adapter protein Grb2. Upon activation of Jurkat T cells via the TCR-CD3 complex, we find that high-affinity binding of Cbl requires the N-terminal SH3 domain of GST-Grb2 fusion protein but after cross-linking of the TCR-CD3 and CD4 receptors, Cbl binds equally to its SH2 domain. Grb2 antisera also precipitated p85 from serum-starved cells, while TCR activation increased p85 and tyrosine-phosphorylated Cbl but not Cbl protein in Grb2 immunocomplexes. Phosphatidylinositol (PI) 3-kinase activity was immunoprecipitated from serum-starved cells with Cbl and to a lesser extent with Grb2 antisera, and TCR cross-linking increased this activity severalfold. The PI 3-kinase activity associated with Cbl amounted to 5 to 10% of the total cellular activity that could be precipitated by p85 antisera. The Ras exchange factor Son-of-sevenless 1 (Sos-1) was not found in anti-Cbl immunoprecipitates from activated cells, and Cbl was not detectable in anti-Sos-1 precipitates, supporting the likelihood that Sos-Grb2 and Cbl-Grb2 are present as distinct complexes. Taken together, these data suggest that Cbl function in Jurkat T cells involves its constitutive association with Grb2 and its recruitment of PI 3-kinase in response to TCR activation