Bijective Proofs of Gould's and Rothe's Identities

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.Comment: 4 page

Carbon Concentration Dependence of the Superconducting Transition Temperature and Structure of MgCxNi3

The crystal structure of the superconductor MgCxNi3 is reported as a function of carbon concentration determined by powder neutron diffraction. The single-phase perovskite structure was found in only a narrow range of carbon content, 0.88 < x < 1.0. The superconducting transition temperature was found to decrease systematically with decreasing carbon concentration. The introduction of carbon vacancies has a significant effect on the positions of the Ni atoms. No evidence for long range magnetic ordering was seen by neutron diffraction for carbon stoichiometries within the perovskite phase stability range.Comment: 4 figure

Test of the Skyrme Effective Field Theory Using Quenched Lattice QCD

The Skyrme effective field theory is tested by evaluating nucleon ground state matrix elements of the correlation functions for two flavor density operators and two pseudoscalar density operators in the Skyrme model and comparing them with results in quenched lattice QCD. The possiblility of using quenched lattice QCD to study higher-order terms in effective field theory is also discussed.Comment: 20 pages in TeX, 6 figures added using "figures", MIT-CTP-200

Observation of a linear temperature dependence of the critical current density in a Ba_{0.63}K_{0.37}BiO_3 single crystal

For a Ba_{0.63}K_{0.37}BiO_3 single crystal with T_c=31 K, H_{c1}=750 Oe at 5 K, and dimensions 3x3x1 mm^3, the temperature and field dependences of magnetic hysteresis loops have been measured within 5-25 K in magnetic fields up to 6 Tesla. The critical current density is J_c(0)=1.5 x 10^5 A/cm^2 at zero field and 1 x 10^5 A/cm^2 at 1 kOe at 5 K. J_c decreases exponentially with increasing field up to 10 kOe. A linear temperature dependence of J_c is observed below 25 K, which differs from the exponential and the power-law temperature dependences in high-Tc superconductors including the BKBO. The linear temperature dependence can be regarded as an intrinsic effect in superconductors.Comment: RevTex, Physica C Vol. 341-348, 729 (2000

Critical current degradation in HTS wires due to cyclic mechanical strain

HTS wires, which may be used in many devices such as magnets and rotating machines, may be subjected to mechanical strains from electromagnetic, thermal and centripetal forces. In some applications these strains will be repeated several thousand times during the lifetime of the device. We have measured critical current degradation due to repeated strain cycles for both compressive and tensile strains. Results for BSCCO-2223 HTS conductor samples are presented for strain values up to 0.5% and cycle numbers up to and beyond 10/sup 4/

Erosion resistance of laser clad Ti-6Al-4V/WC composite for waterjet tooling

AbstractIn waterjet operations, milled surfaces are left with some undesirable dimensional artefacts, thus the use of abrasion resistant mask has been proposed to improve the surface quality of machined components. In this study, the erosion performance of laser clad Ti-6Al-4V/WC composite coating subjected to plain water jet (PWJ) and abrasive water jet (AWJ) impacts to evaluate its potentials for use as waterjet impact resistant mask material and coating on components was investigated. Results showed that composite with 76wt.% WC composition subjected to PWJ and AWJ impacts offered resistance to erosion up to 13 and 8 times that of wrought Ti-6Al-4V respectively. Scanning electron microscopy (SEM) examination of the eroded composite surfaces showed that the erosion mechanism under PWJ impacts is based on the formation of erosion pits, tunnels and deep cavities especially in the interface between the WC particles and the composite matrix owing to lateral outflow jetting and hydraulic penetration. Composite suffered ploughing of the composite matrix, lateral cracking and chipping of embedded WC particles and WC pull-out under AWJ impacts. The composite performance is attributed to the embedded WC particles and the uniformly distributed nano-sized reaction products (TiC and W) reinforcing the ductile β-Ti composite matrix, with its mean hardness enhanced to 6.1GPa. The capability of the Ti-6Al-4V/WC composite coating was demonstrated by effective replication of a pattern on a composite mask to an aluminium plate subjected to selective milling by PWJ with an overall depth of 344μm. Thus, composite cladding for tooling purpose would make it possible to enhance the lifetime of jigs and fixtures and promote rapid machining using the water jet technique

Quantitative mitochondrial DNA copy number determination using droplet digital PCR with single cell resolution

Mitochondria are involved in a number of diverse cellular functions, including energy production, metabolic regulation, apoptosis, calcium homeostasis, cell proliferation, and motility, as well as free radical generation. Mitochondrial DNA (mtDNA) is present at hundreds to thousands of copies per cell in a tissue-specific manner. mtDNA copy number also varies during aging and disease progression and therefore might be considered as a biomarker that mirrors alterations within the human body. Here, we present a new quantitative, highly sensitive droplet digital PCR (ddPCR) method, droplet digital mitochondrial DNA measurement (ddMDM), to measure mtDNA copy number not only from cell populations but also from single cells. Our developed assay can generate data in as little as 3 h, is optimized for 96-well plates, and also allows the direct use of cell lysates without the need for DNA purification or nuclear reference genes. We show that ddMDM is able to detect differences between samples whose mtDNA copy number was close enough as to be indistinguishable by other commonly used mtDNA quantitation methods. By utilizing ddMDM, we show quantitative changes in mtDNA content per cell across a wide variety of physiological contexts including cancer progression, cell cycle progression, human T cell activation, and human aging