On the reduction of the degree of linear differential operators

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type

Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..Comment: 33 pages, this version coincides with the published on

Long-term collateral effects of parent programs on child maltreatment proxies:Can administrative data provide useful insights?

Collecting child maltreatment data from participants is expensive and time-consuming, and often suffers from substantial attrition rates. Administrative population data may prove fruitful to overcome these barriers. The aim of this study was twofold: (1) to illustrate how administrative data may be used in evaluating long-term intervention effects; and (2) to examine collateral effects of three preventive early childhood interventions offered to families in the Netherlands (Supportive Parenting, VoorZorg, and Incredible Years). Using population data, four proxies of child maltreatment were assessed to examine collateral intervention effects: incidences of child protection orders, placements of children in residential care, crime victimization of children or their parents, and parental registrations as a crime suspect. The results revealed no significant differences between experimental and control conditions on any of these proxies, with very small effect sizes (ranging from Cramer's V = 0.01 to Cramer's V = 0.10). We conclude that the results do not provide support for collateral effects, but that studying other outcomes may provide this support. We further discuss that small sample sizes and low prevalences challenge studies using administrative data. Notwithstanding these limitations, we conclude that administrative data can strengthen the evidence base for collateral and direct intervention effects.</p

A rigidity property of asymptotically simple spacetimes arising from conformally flat data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.Comment: 37 page

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Effect of Fluorine and Nitrogen Anions on Properties of Ca-Si-Al-O Glasses

The preparation of bulk glasses in Ca-Si-Al-O-N-F system with the composition in equivalent % of 28e/oCa:56e/oSi:16e/oAl:100-X-Ye/oO:Xe/oF:Ye/oN are reported. The glass formation behaviour and properties of this new range of glasses are examined in detail. Fluorine decreases the glass transition temperature, the density and the mechanical properties of the glasses while nitrogen increases them. Therefore, it appears that fluorine acts as a network modifier while, on the contrary, nitrogen acts as a network former even in presence of fluorine