Moments of the characteristic polynomial in the three ensembles of random matrices

Moments of the characteristic polynomial of a random matrix taken from any of the three ensembles, orthogonal, unitary or symplectic, are given either as a determinant or a pfaffian or as a sum of determinants. For gaussian ensembles comparing the two expressions of the same moment one gets two remarkable identities, one between an $n\times n$ determinant and an $m\times m$ determinant and another between the pfaffian of a $2n\times 2n$ anti-symmetric matrix and a sum of $m\times m$ determinants.Comment: tex, 1 file, 15 pages [SPhT-T01/016], published J. Phys. A: Math. Gen. 34 (2001) 1-1

Therapy Options for Winged Scapula Patients: A Literature Review

Winged scapula is a condition characterized by lateral or medial protrusion of the scapula caused by nerve damage leading to muscular paralysis. The purpose of this systematic review of literature is to evaluate the current research literature related to the effectiveness of therapy options for winged scapula. Eleven peer reviewed English language research articles published from 1998 to present were included for evaluation. Study results revealed positive therapeutic outcomes for physical therapy and scapular bracing. Results also showed positive outcomes for the use of transcutaneous electrical nerve stimulation and acupuncture for the treatment of nerve related conditions similar to winged scapula. Additional research is needed to evaluate the effectiveness of transcutaneous electrical nerve stimulation and acupuncture for winged scapula patients specifically

On possible superconductivity in the doped ladder compound La_(1-x)Sr_xCuO_2.5

LaCuO_2.5 is a system of coupled, two-chain, cuprate ladders which may be doped systematically by Sr substitution. Motivated by the recent synthesis of single crystals, we investigate theoretically the possibility of superconductivity in this compound. We use a model of spin fluctuation-mediated superconductivity, where the pairing potential is strongly peaked at \pi in the ladder direction. We solve the coupled gap equations on the bonding and antibonding ladder bands to find superconducting solutions across the range of doping, and discuss their relevance to the real material.Comment: RevTex, 4 pages, 7 figure

Interplay between shear loading and structural aging in a physical gel

We show that the aging of the mechanical relaxation of a gelatin gel exhibits the same scaling phenomenology as polymer and colloidal glasses. Besides, gelatin is known to exhibit logarithmic structural aging (stiffening). We find that stress accelerates this process. However, this effect is definitely irreducible to a mere age shift with respect to natural aging. We suggest that it is interpretable in terms of elastically-aided elementary (coil$\to$helix) local events whose dynamics gradually slows down as aging increases geometric frustration

Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

Susceptibility of the Endangered Karner Blue Butterfly (Lepidoptera: Lycaenidae) to \u3ci\u3eBacillus Thuringiensis\u3c/i\u3e Var. \u3ci\u3eKurstaki\u3c/i\u3e Used for Gypsy Moth Suppression in Michigan

We investigated the phenological and physiological susceptibility of the endangered Karner blue butterfly (Lycaeides melissa samuelis) to Bacillus thuringiensis var. kurstaki (Bt), a product widely used for gypsy moth (Lymantria dispar) suppression in Michigan and other infested states. We monitored phenology of the bivoltine Karner blue in two regions of Michigan from 1993 to 1995 to determine if larval stages overlapped temporally with the period of Bt application for gypsy moth suppression. Karner blue larvae of the spring generation were found during the period that Bt was applied in nearby areas in 1993 only. However, spring-generation adults or newly laid eggs were observed up to 11 days before applications in 1994 and 1995. Since Karner blue eggs develop within one week, summer-generation larvae were most likely present during or shortly after 1994 and 1995 Bt application periods. These larvae would have been at risk, assuming Bt persistence of 4 to 6 days. Physiological susceptibility of Karner blue larvae to Bt was determined in a laboratory bioassay. Larvae were reared on wild lupine (Lupinus perennis) foliage that was untreated, or sprayed with Bt formulations at rates of 30-37 or 90 BIU/ha. A similar bioassay with second instar gypsy moth larvae on similarly treated white oak (Quercus alba) foliage was conducted concurrently. Karner blue survival was 100%, 27% and 14% on control, low and high Bt treatments, respectively. Early and late Karner blue instars were equally susceptible to Bt. Survival of gypsy moth was 80%, 33% and 5% on control, low and high Bt treatments, respectively, and did not differ significantly from Karner blue survival. We conclude that Karner blue is both phenologically and physiologically susceptible to Bt used for gypsy moth suppression, although the larval generation at risk and extent of phenological overlap may vary from year to year