On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

Texture, realism, performance: exploring the intersection of transtexts and the contemporary sitcom

Contemporary US sitcom is at an interesting crossroads: it has received an increasing amount of scholarly attention (e.g. Mills 2009; Butler 2010; Newman and Levine 2012; Vermeulen and Whitfield 2013), which largely understands it as shifting towards the aesthetically and narratively complex. At the same time, in the post-broadcasting era, US networks are particularly struggling for their audience share. With the days of blockbuster successes like Must See TV’s Friends (NBC 1994-2004) a distant dream, recent US sitcoms are instead turning towards smaller, engaged audiences. Here, a cult sensibility of intertextual in-jokes, temporal and narrational experimentation (e.g. flashbacks and alternate realities) and self-reflexive performance styles have marked shows including Community (NBC 2009-2015), How I Met Your Mother (CBS 2005-2014), New Girl (Fox 2011-present) and 30 Rock (NBC 2006-2013). However, not much critical attention has so far been paid to how these developments in textual sensibility in contemporary US sitcom may be influenced by, and influencing, the use of transmedia storytelling practices, an increasingly significant industrial concern and rising scholarly field of enquiry (e.g. Jenkins 2006; Mittell 2015; Richards 2010; Scott 2010; Jenkins, Ford and Green 2013). This chapter investigates this mutual influence between sitcom and transmedia by taking as its case studies two network shows that encourage invested viewership through their use of transtexts, namely How I Met Your Mother (hereafter HIMHM) and New Girl (hereafter NG). As such, it will pay particular attention to the most transtextually visible character/actor from each show: HIMYM’s Barney Stinson, played by Neil Patrick Harris, and NG’s Schmidt, played by Max Greenfield. This chapter argues that these sitcoms do not simply have their particular textual sensibility and also (happen to) engage with transmedia practices, but that the two are mutually informing and defining. This chapter explores the relationships and interplay between sitcom aesthetics, narratives and transmedia storytelling (or industrial transtexts), focusing on the use of multiple delivery channels in order to disperse “integral elements of a fiction” (Jenkins, 2006 95-6), by official entities such as the broadcasting channels. The chapter pays due attention to the specific production contexts of both shows and how these inform their approaches to transtexts. This chapter’s conceptual framework will be particularly concerned with how issues of texture, the reality envelope and accepted imaginative realism, as well as performance and the actor’s input inform and illuminate contemporary sitcoms and transtexts, and will be the first scholarly research to do so. It will seek out points of connections between two (thus far) separate strands of scholarship and will move discussions on transtexts beyond the usual genre studied (i.e. science-fiction and fantasy), as well as make a contribution to the growing scholarship on contemporary sitcom by approaching it from a new critical angle. On the basis that transmedia scholarship stands to benefit from widening its customary genre choice (i.e. telefantasy) for its case studies and from making more use of in-depth close analysis in its engagement with transtexts, the chapter argues that notions of texture, accepted imaginative realism and the reality envelope, as well as performance and the actor’s input deserve to be paid more attention to within transtext-related scholarship.

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics. Copyright (C) EPLA, 2011

Newton`s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton`s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Improved Prediction of Hydrocarbon Flash Points from Boiling Point Data

Flash points (T(FP)) of hydrocarbons are calculated from their flash point numbers, N(FP), with the relationship T(FP) (K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 In turn, the N(FP) values can be predicted from experimental boiling point numbers (Y(BP)) and molecular structure with the equation N(FP) = 0.987 Y(BP) + 0.176D + 0.687T + 0.712B - 0.176 where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. For a data set consisting of 300 diverse hydrocarbons, the average absolute deviation between the literature and predicted flash points was 2.9 K.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Simple Method to Evaluate and to Predict Flash Points of Organic Compounds

Flash points (T(FP)) of organic compounds are calculated from their flash point numbers, N(FP), with the relationship T(FP) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901. In turn, the N(FP) values can be predicted from boiling point numbers (Y(BP)) and functional group counts with the equation N(FP) = 0.974Y(BP) + Sigma(i)n(i)G(i) + 0.095 where G(i) is a functional group-specific contribution to the value of N(FP) and n(i) is the number of such functional groups in the structure. For a data set consisting of 1000 diverse organic compounds, the average absolute deviation between reported and predicted flash points was less than 2.5 K.

Det är värre att inte börja studera än att hoppa av: En fenomenologisk studie om hur icke traditionella studenter upplever studieavhopp från högskoleutbildning

In Sweden we have the highest rate of nontraditional students among Europe. Coincidently, we also have the highest rates of drop outs among OECD. In this particular field, drop out from higher education, there is a need fore more qualitative studies that can support the "statistics". Studies about experiences of drop outs are significant for society, university and individual. The aim of this study is to describe and understand how nontraditional student experiences drop out from higher education. What do they tell regarding their meeting with the university? How is the drop out visible before the decision to quit? How can the way forward to the drop out be described? What does the university mean for them? The theoretical point of departure is the concept lifeworld and the method is phenomenological hermeneutic with narrative interviews with 5 students. The result points out that the meeting with the university implies a meeting with other individuals, and also a "meeting" within the student himself, by inner questioning and reflection. The students’ relationship to the studies is characterized by the experience of understanding. The dropouts are visible through different events. The decision per se has increased over time and the students have also grown personally by the decision. To understand or not understand is crucial for the experience of learning. The drop out can also be seen as a transition and a turning point. The drop out is an effort and takes place without professional staff, therefore needs to be discussed in public.