On the comparison of two numerical methods for conformal mapping

Let G be a simply-connected domain in the t—plane (t = x + iy), bounded by the three straight lines x = 0, y = 0, x =1 and a Jordan arc with cartesian equation y = τ (X). Also, let g be the function which maps conformally a rectangle R onto G, so that the four corners of R are mapped onto those of G. In this paper we show that the method con-sidered recently by Challis and Burley [2], for determining approx- imations to g, is equivalent to a special case of the well-known method of Garrick [8] for the mapping of doubly-connected domains, Hence, by using results already available in the literature, we provide some theoretical justification for the method of [2]

Homogeneity of pristine and bromine intercalated graphite fibers

Wide variations in the resistivity of intercalated graphite fibers and to use these materials for electrical applications, their bulk properties must be established. The homogeneity of the diameter, the resistivity, and the mass density of 50 graphite fibers, before and after bromine intercalation was measured. Upon intercalation the diameter was found to expand by about 5%, the resistivity to decrease by a factor of five, and the density to increase by about 6%. Each individual fiber was found to have uniform diameter and resistivity over macroscopic regions for lengths as long as 7 cm. The ratio of pristine to intercalated resistivity increases as the pristine fiber diameter increases at a rate of 0.16 micron, but decreases with the increasing ratio of intercalated diameter to pristine diameter at a rate of 0.08

Environmental stability of intercalated graphite fibers

Graphite fibers intercalated with bromine, iodine monochloride, ferric chloride, and cupric chloride were subjected to stability tests under four environments which are encountered by engineering materials in the aerospace industry: ambient laboratory conditions, as would be experienced during handling operations and terrestrial applications; high vacuum, as would be experienced in space applications; high humidity, as would be experienced in marine applications; and high temperature, as would be experienced in some processing steps and applications. Monitoring the resistance of the fibers at ambient laboratory conditions revealed that only the ferric chloride intercalated fibers were unstable, due to absorption of water from the air. All four types of intercalated fibers were unstable, due to absorption of water from the air. All four types of intercalated fibers were stable for long periods under high vacuum. Ferric chloride, cupric chloride, and iodine monochloride intercalated fibers were sensitive to high humidity conditions. All intercalated fibers began to degrade above 250 C. The order of their thermal stability, from lowest to highest, was cupric chloride, iodine monochloride, bromine, and ferric chloride. Of the four types of intercalated fibers tested, the bromine intercalated fibers appear to have the most potential for application, based on environmental stability

PAM Heterozygosity Disrupts Amygdalar Neurophysiology And Copper Homeostasis With Behavioral Consequences

Peptidylglycine α-amidating monooxygenase (PAM) is a secretory granule membrane protein whose luminal enzymatic domains catalyze the Cu-dependent amidation biosynthetic step common to many neuroactive peptides. Aside from its essential role as the sole mammalian amidating enzyme, PAM alters Cu homeostasis, modulates transcription and regulates secretory granule trafficking. The model of PAM haploinsufficiency employs mice heterozygous for the Pam gene (PAM+/-); the mice show anxiety-like disorders and deficiencies in fear learning and memory. We performed whole-cell recordings of pyramidal neurons in the PAM+/- amygdala to elucidate neurophysiological correlates of the fear behavioral phenotypes. Consistent with these observations, thalamic afferent synapses in the PAM+/- lateral nucleus were deficient in long-term potentiation (LTP). This deficit was apparent in the absence and presence of the GABAA receptor antagonist picrotoxin and was abolished when both GABAA and GABAB receptors were blocked. Dietary Cu supplementation rescued the cued learned-fear deficits of PAM+/- mice, with little effect on the behaviors of wildtype mice. Dietary Cu supplementation also corrected the LTP deficit of PAM+/- mice in vitro. Bath application of the extracellular specific Cu chelator bathocuproine disulfonate abolished LTP in wildtype and PAM+/- amygdalae, demonstrating a vital role for Cu in amygdalar synaptic plasticity. Dietary Cu supplementation had no effect on brain Cu or PAM levels, therefore PAM+/- behavioral deficiencies do not result from insufficient Cu and/or PAM. Localization of the major neuronal Cu transporter, ATP7A, was altered in the PAM+/- brain. In addition, quantitative PCR revealed region-specific deficits in Atox-1 and ATP7A that may account for the physiological and behavioral defects associated with PAM heterozygosity. These data indicate that Cu is necessary for normal amygdalar synaptic function, suggesting the PAM+/- behavioral and physiological phenotype stems from dysregulated Cu secretion. Additional studies include analyses of serum Cu and PAM in a population of frail elderly men and electrophysiological study of hippocampal and nucleus accumbens neuronal membrane and synaptic properties in Kalirin7 null mice. Future directions to test the hypothesis of a direct role for PAM in regulating neuronal Cu secretion and explore the essential role of Cu at amygdala afferent synapses are outlined

Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields

The Tomita-Takesaki modular groups and conjugations for the observable algebras of space-like wedges and the vacuum state are computed for translationally covariant, but possibly not Lorentz covariant, generalized free quantum fields in arbitrary space-time dimension d. It is shown that for $d\geq 4$ the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig and Summers \cite{BDFS}, Lorentz covariance and wedge duality are all equivalent in these models. The same holds for d=3 if there is a mass gap. For massless fields in d=3, and for d=2 and arbitrary mass, CGMA does not imply Lorentz covariance of the field itself, but only of the maximal local net generated by the field

New Measurements of Fine-Scale CMB Polarization Power Spectra from CAPMAP at Both 40 and 90 GHz

We present new measurements of the cosmic microwave background (CMB) polarization from the final season of the Cosmic Anisotropy Polarization MAPper (CAPMAP). The data set was obtained in winter 2004-2005 with the 7 m antenna in Crawford Hill, New Jersey, from 12 W-band (84-100 GHz) and 4 Q-band (36-45 GHz) correlation polarimeters with 3.3' and 6.5' beamsizes, respectively. After selection criteria were applied, 956 (939) hours of data survived for analysis of W-band (Q-band) data. Two independent and complementary pipelines produced results in excellent agreement with each other. A broad suite of null tests as well as extensive simulations showed that systematic errors were minimal, and a comparison of the W-band and Q-band sky maps revealed no contamination from galactic foregrounds. We report the E-mode and B-mode power spectra in 7 bands in the range 200 < l < 3000, extending the range of previous measurements to higher l. The E-mode spectrum, which is detected at 11 sigma significance, is in agreement with cosmological predictions and with previous work at other frequencies and angular resolutions. The BB power spectrum provides one of the best limits to date on B-mode power at 4.8 uK^2 (95% confidence).Comment: 19 pages, 17 figures, 2 tables, submitted to Ap

Genetic Determinants of Amidating Enzyme Activity and its Relationship with Metal Cofactors in Human Serum

Abstract BACKGROUND: α-amidation is a final, essential step in the biosynthesis of about half of all peptide hormones and neurotransmitters. Peptidylglycine α-amidating monooxygenase (PAM), with enzymatic domains that utilize Cu and Zn, is the only enzyme that catalyzes this reaction. PAM activity is detected in serum, but its significance and utility as a clinical biomarker remain unexplored. METHODS: We used well-established enzymatic assays specific for the peptidylglycine-α -hydroxylating monooxygenase (PHM) and peptidyl-α-hydroxyglycine α-amidating lyase (PAL) domains of PAM to quantify amidating activity in the sera of 144 elderly men. Relationships between PHM and PAL activity and serum levels of their respective active-site metals, Cu and Zn, were analyzed. Study participants were also genotyped for eight non-coding single nucleotide polymorphisms (SNPs) in PAM, and relationships between genotype and serum enzyme activity and metal levels were analyzed. RESULTS: Serum PHM and PAL activities were normally distributed and correlated linearly with each other. Serum PAL activity, but not serum PHM activity, correlated with serum Cu; neither activity correlated with serum Zn. Study subjects possessing the minor alleles for rs32680 had lower PHM and PAL activities, and subjects with minor alleles for rs11952361 and rs10515341 had lower PHM activities. CONCLUSIONS: Our results characterize large variation in serum amidating activity and provide unique insight into its potential origin and determinants. Common non-coding polymorphisms affect serum amidating activity and Cu levels. Serum amidating activity should be explored as a biomarker for functionality in the elderly and in additional study groups

MMIC low-noise amplifiers and applications above 100 GHz

In this paper we will present recent work on low noise amplifiers developed for very high frequencies above 100 GHz. These amplifiers were developed with a unique InP-based HEMT MMIC process. The amplifiers have been developed for both cryogenic and room temperature amplifier applications with state-of-art performance demonstrated from 100 GHz to 215 GHz

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

On Taylor series of functions regular in Gaier regions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41617/1/13_2005_Article_BF01899316.pd