Fourier transforms of orbital integrals on the Lie algebra of SL⁡2\operatorname{SL}_2

The Harish-Chandra--Howe local character expansion expresses the characters of reductive, $p$-adic groups in terms of Fourier transforms of nilpotent orbital integrals on their Lie algebras, and Murnaghan--Kirillov theory expresses many characters of reductive, $p$-adic groups in terms of Fourier transforms of semisimple orbital integrals (also on their Lie algebras). In many cases, the evaluation of these Fourier transforms seems intractable; but, for $\operatorname{SL}_2$, the nilpotent orbital integrals have already been computed. In this paper, we use a variant of Huntsinger's integral formula, and the theory of $p$-adic special functions, to compute semisimple orbital integrals.Comment: 35 pages; v2: updated introduction to refer to work of Langland

Topological Jordan decompositions

The notion of a topological Jordan decomposition of a compact element of a reductive p-adic group has proven useful in many contexts. In this paper, we generalise it to groups defined over fairly general discretely-valued fields and prove the usual existence and uniqueness properties, as well as an analogue of a fixed-point result of Prasad and Yu.Comment: 28 page

Stability of character sums for positive-depth, supercuspidal representations

We re-write the character formul{\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder's conjectural positive-depth, unramified, toral supercuspidal L-packets

The Solar Orbiter SPICE instrument: An extreme UV imaging spectrometer

Aims. The Spectral Imaging of the Coronal Environment (SPICE) instrument is a high-resolution imaging spectrometer operating at extreme ultraviolet (EUV) wavelengths. In this paper, we present the concept, design, and pre-launch performance of this facility instrument on the ESA/NASA Solar Orbiter mission. / Methods. The goal of this paper is to give prospective users a better understanding of the possible types of observations, the data acquisition, and the sources that contribute to the instrument’s signal. / Results. The paper discusses the science objectives, with a focus on the SPICE-specific aspects, before presenting the instrument’s design, including optical, mechanical, thermal, and electronics aspects. This is followed by a characterisation and calibration of the instrument’s performance. The paper concludes with descriptions of the operations concept and data processing. / Conclusions. The performance measurements of the various instrument parameters meet the requirements derived from the mission’s science objectives. The SPICE instrument is ready to perform measurements that will provide vital contributions to the scientific success of the Solar Orbiter mission

On the computability of some positive-depth supercuspidal characters near the identity

This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of $p$-adic symplectic and special orthogonal groups, near the identity element. We declare two representations equivalent if their characters coincide on a specific neighbourhood of the identity (which is larger than the neighbourhood on which Harish-Chandra local character expansion holds). We construct a parameter space $B$ (that depends on the group and a real number $r>0$) for the set of equivalence classes of the representations of minimal depth $r$ satisfying some additional assumptions. This parameter space is essentially a geometric object defined over \Q. Given a non-Archimedean local field \K with sufficiently large residual characteristic, the part of the character table near the identity element for G(\K) that comes from our class of representations is parameterized by the residue-field points of $B$. The character values themselves can be recovered by specialization from a constructible motivic exponential function. The values of such functions are algorithmically computable. It is in this sense that we show that a large part of the character table of the group G(\K) is computable

The Effect of Induced Happiness Levels on Academic Performance

Past research has shown that people who have high levels of happiness show greater job performance and productivity than those who are less happy (Lyubomirsky, King, & Diener, et al., 2005) and that happiness can be improved in both non-depressed and depressed people (Sin & Lyubomirsky, 2009; Seligman, Steel, Park, & Peterson., 2005). However, little research has been done on the application of positivity interventions in the classroom context. In 4 academic classrooms, positivity and control interventions were applied. I then measured well-being, engagement, and classroom performance. I found that the positivity intervention resulted in higher engagement and classroom performance for advanced students, but not for introductory students

Strong is the new slim: a study of the body and gender amongst female free weights users

This research explored the importance of the ideal female body and gender stereotypes amongst a group of female free weights users in a fitness facility in Scotland. Utilising principles of ethnography, information was initially gathered through working as a participant-as-observer to identify different female free weights users within the facility. From this, as well as using a gatekeeper and snowball sampling, twenty women took part in one-to-one interviews. Different groups of women were interviewed including: those training in the free weights areas to aid their sporting performance, for health or aesthetic reasons and those preparing for physique competitions. Interviews focused on the women’s use of the free weights areas, perceptions of their own bodies and their opinions on the ideal female body as well as their interpretations of the concepts femininity, masculinity and muscularity. The unique narrative of each woman was critically analysed with reference to social construction feminism. Whilst interviews were the main data collection technique for this research, participant observation and informal conversations within the free weights areas also informed the findings of this study. The motivations behind women taking part in weight training are presented. Interviewees’ definitions of the ideal female body are explored and the significance of this body is discussed. Factors influencing the women’s definitions of the ideal body are also examined. The impact of social media on participants’ use of the free weights areas is analysed. The women’s perceptions of the terms masculinity, femininity and muscularity are considered alongside how these perceptions affected their training within the free weights areas