Spectral behaviour of a simple non-self-adjoint operator

We investigate the spectrum of a typical non-self-adjoint differential operator $AD=-d^2/dx^2\otimes A$ acting on \Lp(0,1)\otimes \mathbb{C}^2, where $A$ is a $2\times 2$ constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of $[0,1]\subset\mathbb{R}$. For $A\in \mathbb{R}^{2\times 2}$ we explore in detail the connection between the entries of $A$ and the spectrum of $AD$, we find necessary conditions to ensure similarity to a self-adjoint operator and give numerical evidence that suggests a non-trivial spectral evolution.Comment: 42 pages, 6 figure

On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding

The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity. This ensures that the resolvent of the bosonic Hamiltonian is compact. We find an upper bound for the asymptotic distribution of the eigenvalues.Comment: 11 pages, LaTe

Supersymmetric exact sequence, heat kernel and super KdV hierarchy

We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations. We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super KdV hierarchy. We combine this algebraic approach with an analytic analysis of the super heat operator.We obtain the explicit expression for the Green's function of the super heat operator in terms of a series expansion and discuss its properties. The expansion is convergent under the assumption of bounded bosonic and fermionic potentials. We show that the asymptotic expansion when $t\to0^+$ of the Green's function for the super heat operator evaluated over its diagonal generates all the members of the N=1 super KdV hierarchy.Comment: 20 pages, to be published in JM

Non-abelian D=11 Supermembrane

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes.Comment: Contribution to the Proceedings of the Dubna International SQS'09 Workshop ("Supersymmetries and Quantum Symmetries-2009", July 29 - August 3, 2009. 12pg, Late

Trends in childhood pneumococcal vaccine coverage in Shanghai, China, 2005–2011: a retrospective cohort study

Abstract Background In China, the pneumococcal conjugate vaccine (PCV7) and the pneumococcal polysaccharide vaccine (PPSV23) are not offered under the government’s Expanded Program on Immunization and are instead administered for a fee. PCV7 is more effective and covers more serotypes associated with invasive disease in children, but is also more expensive, than PPSV23. Because of their expense, there is concern that these vaccines, especially PCV7, have low uptake particularly among non-locals, migrants from outside of Shanghai. This paper characterizes the differential coverage of PCV7 and PPSV23 between locals and non-locals in Shanghai, and illustrates coverage trends over time. Methods In this retrospective cohort study, children born between 2005 and 2011 were sampled from the Shanghai Immunization Program Information System. Bivariate and multivariable analyses examined the relationships between demographic characteristics, residency status (non-locals vs locals), and vaccination coverage. Results PPSV23 coverage (29.8 %) among children over 2 years of age was higher than PCV7 coverage (10.1 %) for locals and non-locals. Uptake of PCV7 increased substantially after children were 2 years of age. Overall, non-local populations had higher PPSV23 coverage (OR: 1.34; 98 % CI: 1.22, 1.46) but lower PCV7 coverage (OR: 0.617, 98 % CI: 0.547, 0.695) than locals. Conclusions There is a need for increasing overall pneumococcal coverage in Shanghai children, particularly with the more effective PCV7 vaccine. Morbidity and mortality due to invasive pneumococcal disease for children <1 year of age are unlikely to be mitigated if the current age-related vaccination patterns are not improved.http://deepblue.lib.umich.edu/bitstream/2027.42/117253/1/12889_2016_Article_2785.pd

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Exploring the currency of violence in Serious Organised Crime (SOC)

Book Chapte

The response of perennial and temporary headwater stream invertebrate communities to hydrological extremes

The headwaters of karst rivers experience considerable hydrological variability, including spates and streambed drying. Extreme summer flooding on the River Lathkill (Derbyshire, UK) provided the opportunity to examine the invertebrate community response to unseasonal spate flows, flow recession and, at temporary sites, streambed drying. Invertebrates were sampled at sites with differing flow permanence regimes during and after the spates. Following streambed drying at temporary sites, dewatered surface sediments were investigated as a refugium for aquatic invertebrates. Experimental rehydration of these dewatered sediments was conducted to promote development of desiccation-tolerant life stages. At perennial sites, spate flows reduced invertebrate abundance and diversity, whilst at temporary sites, flow reactivation facilitated rapid colonisation of the surface channel by a limited number of invertebrate taxa. Following streambed drying, 38 taxa were recorded from the dewatered and rehydrated sediments, with Oligochaeta being the most abundant taxon and Chironomidae (Diptera) the most diverse. Experimental rehydration of dewatered sediments revealed the presence of additional taxa, including Stenophylax sp. (Trichoptera: Limnephilidae) and Nemoura sp. (Plecoptera: Nemouridae). The influence of flow permanence on invertebrate community composition was apparent despite the aseasonal high-magnitude flood events

On Non Commutative G2 structure

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras. We show that there are eight possible solutions for this extended structure, one of which corresponds to the commutative case. Then we obtain a matrix representation solving such algebras using combinatorial arguments. An application to matrix model of M-theory is discussed.Comment: 16 pages, Latex. Typos corrected, minor changes. Version to appear in J. Phys.A: Math.Gen.(2005