On the oscillation of solutions and existence of positive solutions of neutral difference equations

AbstractWe obtain sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation Δ(xn + cxn − m) + pnxn − k = 0, n = 0, 1, 2, …, where c and pn are real numbers, m and k are integers, and pn, m and k are nonnegative

Coisotropic deformations of associative algebras and dispersionless integrable hierarchies

The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras. It discusses the link between the structure constants and the Hirota's tau function, and shows that the dispersionless Hirota's bilinear equations are, within this approach, a way of writing the associativity conditions for the structure constants in terms of the tau function. It also suggests a simple interpretation of the algebro-geometric construction of the universal Whitham's equations of genus zero due to Krichever.Comment: minor misprints correcte

Spin Calogero models obtained from dynamical r-matrices and geodesic motion

We study classical integrable systems based on the Alekseev-Meinrenken dynamical r-matrices corresponding to automorphisms of self-dual Lie algebras, ${\cal G}$. We prove that these r-matrices are uniquely characterized by a non-degeneracy property and apply a construction due to Li and Xu to associate spin Calogero type models with them. The equation of motion of any model of this type is found to be a projection of the natural geodesic equation on a Lie group $G$ with Lie algebra ${\cal G}$, and its phase space is interpreted as a Hamiltonian reduction of an open submanifold of the cotangent bundle $T^*G$, using the symmetry arising from the adjoint action of $G$ twisted by the underlying automorphism. This shows the integrability of the resulting systems and gives an algorithm to solve them. As illustrative examples we present new models built on the involutive diagram automorphisms of the real split and compact simple Lie algebras, and also explain that many further examples fit in the dynamical r-matrix framework.Comment: 25 pages, with minor stylistic changes and updated references in v

Generalizations of Felder's elliptic dynamical r-matrices associated with twisted loop algebras of self-dual Lie algebras

A dynamical $r$-matrix is associated with every self-dual Lie algebra \A which is graded by finite-dimensional subspaces as \A=\oplus_{n \in \cZ} \A_n, where \A_n is dual to \A_{-n} with respect to the invariant scalar product on \A, and \A_0 admits a nonempty open subset \check \A_0 for which \ad \kappa is invertible on \A_n if $n\neq 0$ and \kappa \in \check \A_0. Examples are furnished by taking \A to be an affine Lie algebra obtained from the central extension of a twisted loop algebra \ell(\G,\mu) of a finite-dimensional self-dual Lie algebra \G. These $r$-matrices, R: \check \A_0 \to \mathrm{End}(\A), yield generalizations of the basic trigonometric dynamical $r$-matrices that, according to Etingof and Varchenko, are associated with the Coxeter automorphisms of the simple Lie algebras, and are related to Felder's elliptic $r$-matrices by evaluation homomorphisms of \ell(\G,\mu) into \G. The spectral-parameter-dependent dynamical $r$-matrix that corresponds analogously to an arbitrary scalar-product-preserving finite order automorphism of a self-dual Lie algebra is here calculated explicitly.Comment: LaTeX2e, 22 pages. Added a reference and a remar

The effect of the dynamical state of clusters on gas expulsion and infant mortality

The star formation efficiency (SFE) of a star cluster is thought to be the critical factor in determining if the cluster can survive for a significant (>50 Myr) time. There is an often quoted critical SFE of ~30 per cent for a cluster to survive gas expulsion. I reiterate that the SFE is not the critical factor, rather it is the dynamical state of the stars (as measured by their virial ratio) immediately before gas expulsion that is the critical factor. If the stars in a star cluster are born in an even slightly cold dynamical state then the survivability of a cluster can be greatly increased.Comment: 6 pages, 2 figures. Review talk given at the meeting on "Young massive star clusters - Initial conditions and environments", E. Perez, R. de Grijs, R. M. Gonzalez Delgado, eds., Granada (Spain), September 2007, Springer: Dordrecht. Replacement to correct mistake in a referenc

The Large Magellanic Cloud: A power spectral analysis of Spitzer images

We present a power spectral analysis of Spitzer images of the Large Magellanic Cloud. The power spectra of the FIR emission show two different power laws. At larger scales (kpc) the slope is ~ -1.6, while at smaller ones (tens to few hundreds of parsecs) the slope is steeper, with a value ~ -2.9. The break occurs at a scale around 100-200 pc. We interpret this break as the scale height of the dust disk of the LMC. We perform high resolution simulations with and without stellar feedback. Our AMR hydrodynamic simulations of model galaxies using the LMC mass and rotation curve, confirm that they have similar two-component power-laws for projected density and that the break does indeed occur at the disk thickness. Power spectral analysis of velocities betrays a single power law for in-plane components. The vertical component of the velocity shows a flat behavior for large structures and a power law similar to the in-plane velocities at small scales. The motions are highly anisotropic at large scales, with in-plane velocities being much more important than vertical ones. In contrast, at small scales, the motions become more isotropic.Comment: 8 pages, 4 figures, talk presented at "Galaxies and their Masks", celebrating Ken Freeman's 70-th birthday, Sossusvlei, Namibia, April 2010. To be published by Springer, New York, editors D.L. Block, K.C. Freeman, & I. Puerar

Distribution of MHC class II alleles in primary systemic vasculitis

Distribution of MHC class II alleles in primary systemic vasculitis. Previous studies have shown a number of different associations between major histocompatibility complex (MHC) alleles and primary systemic vasculitis. Disease heterogeneity and the lack of specificity of certain MHC typing techniques may have contributed to the lack of consistency in those studies. We therefore studied a relatively homogeneous group of 94 patients with Wegener's granulomatosis, microscopic polyangiitis, or renal-limited vasculitis using molecular techniques that allow more precise assignment of MHC genotype. DNA was prepared from peripheral blood and DRB1 genotype determined by Taq restriction fragment length polymorphism. DQB1 and DPB1 genotype were assigned by polymerase chain reaction amplification followed by probing with allele-specific oligonucleotides. Specificity of associated anti-neutrophil cytoplasm antibodies (ANCA) was determined where possible by solid phase immunoassays using purified proteinase 3 (PR3) and myeloperoxidase (MPO). After correction for multiple comparisons there were no significant differences in the distribution of DRB1, DQB1 and DPB1 alleles between a local control group (N = 90 for DRB1, N = 50 for DQB1 and DPB1) and the patient group as a whole (N = 94) or two a priori defined subgroups (anti-PR3 positive, N = 35; anti-MPO positive, N = 22). We have therefore found no significant association between primary systemic vasculitis and any MHC class II allele. This, together with the fact that previous smaller studies have shown no consistent association, suggests that any such association is very weak, if it exists at all

A comparison study of geostatistical simulation for predicting soil texture

Non-Peer Reviewe

Understanding the relationship between breastfeeding and postnatal depression: the role of pain and physical difficulties

AIMS: To examine the relationship between specific reasons for stopping breastfeeding and depressive symptoms in the postnatal period. BACKGROUND: Difficulty breastfeeding has been connected to postnatal depression although it is unclear whether difficulty breastfeeding precedes or succeeds a diagnosis. However, the concept of ‘breastfeeding difficulty’ is wide and includes biological, psychological and social factors. DESIGN: A cross‐sectional self‐report survey. METHODS: Data were collected between December 2012 and February 2013. 217 women with an infant aged 0‐6 months who had started breastfeeding at birth but had stopped before 6 months old completed a questionnaire examining breastfeeding duration and reasons for stopping breastfeeding. They further completed a copy of the Edinburgh Postnatal Depression Scale. RESULTS: A short breastfeeding duration and multiple reasons for stopping breastfeeding were associated with higher depression score. However, in a regression analysis only the specific reasons of stopping breastfeeding for physical difficulty and pain remained predictive of depression score. CONCLUSIONS: Understanding women's specific reasons for stopping breastfeeding rather than breastfeeding duration is critical in understanding women's breastfeeding experience and providing women with emotional support. Issues with pain and physical breastfeeding were most indicative of postnatal depression in comparison to psychosocial reasons highlighting the importance of spending time with new mothers to help them with issues such as latch

Explicit description of twisted Wakimoto realizations of affine Lie algebras

In a vertex algebraic framework, we present an explicit description of the twisted Wakimoto realizations of the affine Lie algebras in correspondence with an arbitrary finite order automorphism and a compatible integral gradation of a complex simple Lie algebra. This yields generalized free field realizations of the twisted and untwisted affine Lie algebras in any gradation. The free field form of the twisted Sugawara formula and examples are also exhibited.Comment: 24 pages, LaTeX, v2: small corrections in appendix