Petrophysical Variation in Central North Sea Fields

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Deformations of overconvergent isocrystals on the projective line

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent isocrystals on $U$ with fixed "local monodromy" along $Z$. En route, we show that a Hochschild cochain complex governs deformations of a module over an arbitrary associative algebra. We also relate this Hochschild cochain complex to a de Rham complex in order to understand the deformation theory of a differential module over a differential ring.Comment: 59 pages; fixed typos, improved exposition; comments welcome

Samplers and Extractors for Unbounded Functions

Blasiok (SODA\u2718) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions f from {0,1}^m to the real numbers such that f(U_m) has subgaussian tails, and asked for explicit constructions. In this work, we give the first explicit constructions of subgaussian samplers (and in fact averaging samplers for the broader class of subexponential functions) that match the best known constructions of averaging samplers for [0,1]-bounded functions in the regime of parameters where the approximation error epsilon and failure probability delta are subconstant. Our constructions are established via an extension of the standard notion of randomness extractor (Nisan and Zuckerman, JCSS\u2796) where the error is measured by an arbitrary divergence rather than total variation distance, and a generalization of Zuckerman\u27s equivalence (Random Struct. Alg.\u2797) between extractors and samplers. We believe that the framework we develop, and specifically the notion of an extractor for the Kullback-Leibler (KL) divergence, are of independent interest. In particular, KL-extractors are stronger than both standard extractors and subgaussian samplers, but we show that they exist with essentially the same parameters (constructively and non-constructively) as standard extractors

Probing the hadronic phase with resonances of different lifetimes in Pb-Pb collisions with ALICE

The ALICE experiment has measured the production of a rich set of hadronic resonances, such as $\rho(770)^{0}$, ${\rm K}^{\ast}(892)^{0}$, $\phi$(1020), $\Sigma^{\pm}$(1385), $\Lambda(1520)$ and $\Xi^{\ast 0}$ in pp, p-Pb and Pb-Pb collisions at various energies at the LHC. A comprehensive overview and the latest results are presented in this paper. Special focus is given to the role of hadronic resonances for the study of final-state effects in high-energy collisions. In particular, the measurement of resonance production in heavy-ion collisions has the capability to provide insight into the existence of a prolonged hadronic phase after hadronisation. The observation of the suppression of the production of $\Lambda(1520)$ resonance in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV adds further support to the existence of such a dense hadronic phase, as already evidenced by the ratios ${\rm K}^{\ast}(892)^{0}$/${\rm K}$ and $\rho(770)^{0}$/$\pi$.Comment: 4 pages, 3 figures, 17th International Conference on Strangeness in Quark Matter (SQM 2017

Non-Gaussianity of Inflationary Gravitational Waves from the Field Equation

We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green's function, reproducing the results from in-in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.Comment: 17 pages, 2 figures; comments welcom

Coefficient estimates for some classes of functions associated with qq-function theory

In this paper, for every $q\in(0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach type problem for the class of $q$-convex functions of order $\alpha, 0\le\alpha<1$. In addition, we discuss the Fekete-szeg\"o problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to couple of conjectures for the class of $q$-starlike functions of order $\alpha, 0\le\alpha<1$.Comment: 12 page