We study the impact of changing the existing terminology to describe the rules governing Social Security retirement benefits. We provided respondents from a nationally representative online panel with information pertinent to the decision of when to claim Social Security retirement benefits. The content of the information treatments was identical for all respondents, but some were randomly given an alternative set of terms to refer to the key claiming ages (the experimental treatment group), while others were given the current terms (the control group). Despite the minimal nature of the change, there were significant differences in outcomes. Those in the treatment group spent less time reading the information, but their understanding of the Social Security program improved more than the control group. In addition, the treatment delayed retirement claiming intentions by an average of about two and a half months and increased the recommended claiming age to vignette characters by a similar magnitude. The effects were particularly strong for those with low levels of financial literacy. The relative gains in knowledge persisted several months after the treatment.

Two experiments examined moral judgments about a decision-maker’s choices when he chose a sure-thing, 400 out of 600 people will be saved, or a risk, a two-thirds probability to save everyone and a one-thirds probability to save no-one. The results establish a moral echoing effect — a tendency to credit a decision-maker with a good outcome when the decision-maker made the typical choices of the sure-thing in a gain frame or the risk in a loss frame, and to discredit the decision-maker when there is a bad outcome and the decision-maker made the atypical choices of a risk in a gain frame or a sure-thing in a loss frame. The moral echoing effect is established in Experiment 1 (n=207) in which participants supposed the outcome would turn well or badly, and it is replicated in Experiment 2 (n=173) in which they knew it had turned out well or badly, for judgments of moral responsibility and blame or praise. The effect does not occur for judgments of cause, control, counterfactual alternatives, or emotions.

Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. We focus on the curvature inside the individual components of the fabric, which are two orthogonal frames and two orthogonal families of chains. We show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures in each chain are arranged in a quadratic bi-sequence. We also prove a sufficient condition for the fabric to be integral.

We consider three special and significant cases of the following problem. Let $D\subset \mathbb{R}^{d}$ be a (possibly unbounded) set of finite Lebesgue measure. Let $E(\mathbb{Z}^{d})=\{e^{2\unicode[STIX]{x1D70B}ix\cdot n}\}\text{}_{n\in \mathbb{Z}^{d}}$ be the standard exponential basis on the unit cube of $\mathbb{R}^{d}$. Find conditions on $D$ for which $E(\mathbb{Z}^{d})$ is a frame, a Riesz sequence, or a Riesz basis for $L^{2}(D)$.

Neoliberal metaphors of students often describe students as consumers, managers and even as commodities, but this analysis often disregards the discursive complexity of education. We argue that frame merging is essential to understand the hybrid modalities of neoliberal images of students in the Swedish context, where the image of the student is suspended between a social democratic welfare service model, academic capitalism, new public management and welfare nationalism. We demonstrate this through the case study of introducing student fees for non-EU students in Swedish higher education, and how the merging of universal tax financing with a more individualised fee paying solution creates variegated and complex metaphors of students and higher education. These metaphors are infused with social democratic social citizenship, neoliberal reform of welfare services, academic capitalism and nationalist welfare chauvinism. This implies that, in practice, it is nigh on impossible to disentangle the neoliberal consumer metaphor from that of social citizenship; instead they merge to generate multiple contextually relevant metaphors to fit the local debates in higher education.

In this paper, it is proved that every isometry between the unit spheres of two real Banach spaces preserves the frames of the unit balls. As a consequence, if $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}X$ and $Y$ are $n$-dimensional Banach spaces and $T_0$ is an isometry from the unit sphere of $X$ onto that of $Y$ then it maps the set of all $(n-1)$-extreme points of the unit ball of $X$ onto that of $Y$.

A subspace S of Tychonoff space X is relatively pseudocompact in X if every f∈C(X) is bounded on S. As is well known, this property is characterisable in terms of the functor υ which reflects Tychonoff spaces onto the realcompact ones. A device which exists in the category CRegFrm of completely regular frames which has no counterpart in Tych is the functor which coreflects completely regular frames onto the Lindelöf ones. In this paper we use this functor to characterise relative pseudocompactness.

Real ideals of the ring ℜL of real-valued continuous functions on a completely regular frame L are characterized in terms of cozero elements, in the manner of the classical case of the rings C(X). As an application, we show that L is realcompact if and only if every free maximal ideal of ℜL is hyper-real—which is the precise translation of how Hewitt defined realcompact spaces, albeit under a different appellation. We also obtain a frame version of Mrówka’s theorem that characterizes realcompact spaces.

The main purpose of this paper is to develop a point-free notion of topological transitivity. First, we define transitive frame maps and transitive completely prime filters in Frm, the category of frames and frame maps. Then we discuss the relationship between these notions in Frm and the notions of topological transitive and transitive points in Top. Finally, we investigate the relationship between transitive frame maps and the existence of transitive completely prime filters.

A method for constructing a pair of biorthogonal interpolatory multiscaling functions is given and an explicit formula for constructing the corresponding biorthogonal multiwavelets is obtained. A multiwavelet sampling theorem is also established. In addition, we improve the stability of the biorthogonal interpolatory multiwavelet frame by the linear combination of a pair of biorthogonal interpolatory multiwavelets. Finally, we give an example illustrating how to use our method to construct biorthogonal interpolatory multiscaling functions and corresponding multiwavelets.

The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.