A note on log-convexity of q-Catalan numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted

Domain wall switching: optimizing the energy landscape

It has recently been suggested that exchange spring media offer a way to increase media density without causing thermal instability (superparamagnetism), by using a hard and a soft layer coupled by exchange. Victora has suggested a figure of merit xi = 2 E_b/mu_0 m_s H_sw, the ratio of the energy barrier to that of a Stoner-Wohlfarth system with the same switching field, which is 1 for a Stoner-Wohlfarth (coherently switching) particle and 2 for an optimal two-layer composite medium. A number of theoretical approaches have been used for this problem (e.g., various numbers of coupled Stoner-Wohlfarth layers and continuum micromagnetics). In this paper we show that many of these approaches can be regarded as special cases or approximations to a variational formulation of the problem, in which the energy is minimized for fixed magnetization. The results can be easily visualized in terms of a plot of the energy as a function of magnetic moment m_z, in which both the switching field [the maximum slope of E(m_z)] and the stability (determined by the energy barrier E_b) are geometrically visible. In this formulation we can prove a rigorous limit on the figure of merit xi, which can be no higher than 4. We also show that a quadratic anistropy suggested by Suess et al comes very close to this limit.Comment: Acccepted for proceedings of Jan. 2007 MMM Meeting, paper BE-0

Collaboration : a key competence for competing in the 21st century

It is now an accepted fact that in the 21st century competition will be between networks of organisations and individuals, which efficiently and effectively integrate their competencies and resources in order to compete in a global economy (Bititci et al, 2004). Similarly the SME'2000 conference, which was held in Bologna, concluded that 'SMEs belonging to networks are often more competitive and innovative than those operating in isolation. When working together, SMEs can increase their focus through specialisation in functions that are complementary within their networks'

Buffet test in the National Transonic Facility

A buffet test of a commercial transport model was accomplished in the National Transonic Facility at the NASA Langley Research Center. This aeroelastic test was unprecedented for this wind tunnel and posed a high risk for the facility. Presented here are the test results from a structural dynamics and aeroelastic response point of view. The activities required for the safety analysis and risk assessment are described. The test was conducted in the same manner as a flutter test and employed on-board dynamic instrumentation, real time dynamic data monitoring, and automatic and manual tunnel interlock systems for protecting the model

Effects of 3-d and 4-d-transition metal substitutional impurities on the electronic properties of CrO2

We present first-principles based density functional theory calculations of the electronic and magnetic structure of CrO2 with 3d (Ti through Cu) and 4d (Zr through Ag) substitutional impurities. We find that the half-metallicity of CrO2 remains intact for all of the calculated substitutions. We also observe two periodic trends as a function of the number of valence electrons: if the substituted atom has six or fewer valence electrons (Ti-Cr or Zr-Mo), the number of down spin electrons associated with the impurity ion is zero, resulting in ferromagnetic (FM) alignment of the impurity magnetic moment with the magnetization of the CrO2 host. For substituent atoms with eight to ten (Fe-Ni or Ru-Pd with the exception of Ni), the number of down spin electrons contributed by the impurity ion remains fixed at three as the number contributed to the majority increases from one to three resulting in antiferromagnetic (AFM) alignment between impurity moment and host magnetization. The origin of this variation is the grouping of the impurity states into 3 states with approximate "t2g" symmetry and 2 states with approximate "eg" symmetry. Ni is an exception to the rule because a Jahn-Teller-like distortion causes a splitting of the Ni eg states. For Mn and Tc, which have 8 valence electrons, the zero down spin and 3 down spin configurations are very close in energy. For Cu and Ag atoms, which have 11 valence electrons, the energy is minimized when the substituent ion contributes 5 Abstract down-spin electrons. We find that the interatomic exchange interactions are reduced for all substitutions except for the case of Fe for which a modest enhancement is calculated for interactions along certain crystallographic directions.Comment: 26 pages, 10 figures, 2 table

Splitting The Gluon?

In the strongly correlated environment of high-temperature cuprate superconductors, the spin and charge degrees of freedom of an electron seem to separate from each other. A similar phenomenon may be present in the strong coupling phase of Yang-Mills theories, where a separation between the color charge and the spin of a gluon could play a role in a mass gap formation. Here we study the phase structure of a decomposed SU(2) Yang-Mills theory in a mean field approximation, by inspecting quantum fluctuations in the condensate which is formed by the color charge component of the gluon field. Our results suggest that the decomposed theory has an involved phase structure. In particular, there appears to be a phase which is quite reminiscent of the superconducting phase in cuprates. We also find evidence that this phase is separated from the asymptotically free theory by an intermediate pseudogap phase.Comment: Improved discussion of magnetic nature of phases; removed unsubstantiated speculation about color confinemen

Down-regulation of Fas gene expression in colon cancer is not a result of allelic loss or gene rearrangement.

Expression of Fas, an apoptosis-inducing receptor, in colonic epithelium is progressively reduced during malignant transformation. We have examined the human Fas gene for loss of heterozygosity (LOH) and gross rearrangements in colon tumours and matched normal mucosa. Polymerase chain reaction (PCR) primers were designed to span a DraI restriction fragment length polymorphic site in the gene. Heterozygosity was detected in normal DNA samples by PCR amplification of the polymorphic site and restriction enzyme digestion. Thirty-eight of 88 patients (43%) with colon carcinomas were informative for the assay, and LOH was detected in 6 of the 38 (16%) corresponding tumours. Tumours from three patients with LOH did not express detectable Fas mRNA, and Fas expression was reduced or absent in 7 of 11 tumours from informative patients without LOH. Southern blotting of tumour DNA samples was used to detect rearrangement of the Fas gene, but no altered hybridization patterns were observed in 64 tumours analysed. These findings indicate that disruption of the Fas gene is not primarily responsible for the loss of Fas protein expression reported in colon cancer. We have also shown that loss of Fas gene transcription is common in these tumours, which may be due to epigenetic gene silencing

Planetary Bistatic Radar

Planetary radar observations offer the potential for probing the properties of characteristics of solid bodies throughout the inner solar system and at least as far as the orbit of Saturn. In addition to the direct scientific value, precise orbital determinations can be obtained from planetary radar observations, which are in turn valuable for mission planning or spacecraft navigation and planetary defense. The next-generation Very Large Array would not have to be equipped with a transmitter to be an important asset in the world's planetary radar infrastructure. Bistatic radar, in which one antenna transmits (e.g., Arecibo or Goldstone) and another receives, are used commonly today, with the Green Bank Telescope (GBT) serving as a receiver. The improved sensitivity of the ngVLA relative to the GBT would improve the signal-to-noise ratios on many targets and increase the accessible volume specifically for asteroids. Goldstone-ngVLA bistatic observations would have the potential of rivaling the sensitivity of Arecibo, but with much wider sky access.Comment: 11 pages, 2 figures, To be published in the ASP Monograph Series, "Science with a Next-Generation VLA", ed. E. J. Murphy (ASP, San Francisco, CA