[en] The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between the minisuperspace variables and their momenta operators. I extend these deformed commutating relations to the corresponding deformed Poisson algebra. For an exponential dilaton potential, the exact classical and quantum solutions in the commutative and noncommutative cases, and some approximate analytical solutions in the case of GUP, are presented and compared

[en] In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set I⁺(p) intersection I^-(q) whose duration τ(p,q) is short compared with the curvature scale. In the present Letter we obtain asymptotic formulae valid when the point q recedes to the future boundary I⁺ of an asymptotically de Sitter space-time. The volume (at fixed τ) remains finite in this limit and is given by the universal formula V(τ)=4/3 π(2lncosh(τ)/2 -tanh²(τ)/2 ) plus corrections (given by a series in e^-t_q) which begin at order e^-4t_q. The coefficients of the corrections depend on the geometry of I⁺. This behaviour is shown to be consistent with the no-hair property of cosmological event horizons and with calculations of de Sitter quasi-normal modes in the literature

[en] A function f is said to be stable with respect to some property (P) if there exists ε > 0 such that f + ξ fulfill (P) for all linear functional ξ satisfying parallel ξ parallel < ε. S-quasiconvex functions introduced by Phu (Optimization, Vol.38, 1996) are stable with respect to the properties: 'every lower level set is convex', 'each local minimizer is a global minimizer', and 'each stationary point is a global minimizer'. Correspondingly, we introduced the concepts of s-quasimonotone maps and showed that in the case of a differentiable map, s-quasimonotonicity of the gradient is equivalent to s-quasiconvexity of the underlying function. In this paper, strictly s-quasiconvex functions and strictly s-quasimonotone maps are introduced. In the case of a differentiable map, strict s-quasimonotonicity of the gradient is equivalent to strict s-quasiconvexity of the underlying function, too. An algorithm for finding supremum of the set of all ε above of a continuously twice differentiable strictly s-quasiconvex function on R¹ is presented. (author)

[en] In this survey the circle problem is treated in the broad sense, as the problem of the asymptotic properties of the quantity $P(x)$, the remainder term in the circle problem. A survey of recent results in this direction is presented. The main focus is on the behaviour of $P(x)$ on short intervals. Several conjectures on the local behaviour of $P(x)$ which lead to a solution of the circle problem are presented. A strong universality conjecture is stated which links the behaviour of $P(x)$ with the behaviour of the second term in Weyl’s formula for the Laplace operator on a closed Riemannian 2-manifold with integrable geodesic flow.

Bibliography: 43 titles. (paper)

[en] The geometrical meaning of a particularly simple metric in the superspace is elucidated and the possible connection with mechanisms of topological origin in high energy physics is analyzed and discussed. New possible mechanism of the localization of the fields in a particular sector of the supermanifold is proposed and the similarity and differences with a 5-dimensional warped model is shown. The description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of the possible vacuum solutions

[en] We give the exact solution of orbit dependent nuclear pairing problem between two nondegenerate energy levels using the Bethe ansatz technique. Our solution reduces to previously solved cases in the appropriate limits including Richardson's treatment of reduced pairing in terms of rational Gaudin algebra operators

[en] A strategy for the derivation of fast, accurate and stable algorithms for combining the reconstruction and the feature extraction step for solving linear ill-posed problems in just one method is presented. The precomputation of special reconstruction kernels with optimized parameters for the combination of the two tasks allows for fast implementations and better results than separate realizations. The concept of order optimality is generalized to the solution of feature reconstruction and to Banach spaces in order to find criteria for the selection of suitable mollifiers. Results from real data in different tomographic modalities and scanning geometries are presented with the direct calculation of derivatives, as in Canny edge detectors, and the Laplacian of the solution used in many segmentation algorithms. The method works also when the searched-for solution is not smooth or when the data are very noisy. This shows the versatility of the approach

[en] Type IIA flux compactifications with O6-planes have been argued from a four dimensional effective theory point of view to admit stable, moduli free solutions. We discuss in detail the ten dimensional description of such vacua and present exact solutions in the case when the O6-charge is smoothly distributed. In the localised case, the solution is a half-flat, non-Calabi-Yau metric. Finally, using the ten dimensional description we show how all moduli are stabilised and reproduce precisely the results of de Wolfe et al. (author)

[en] The geometry of almost complex manifolds with degenerate indefinite Hermitian metrics is studied

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