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

A STUDY OF THE MESSAGES ON SPICE GIRLS’ SONG LYRIC “GOODBYE”

Literature is human’s expression. It is divided into drama, novel, poem, and also song. Song is one of the literary works that has beautiful words on it like figurative language, diction, and also imagery. The problems of this study are analyzing the detailed, general meaning, and also the messages of Spice Girls’ song “Goodbye”. This study used the descriptive qualitative because this research started with collecting reviewing research literature to provide the data. This research used objective approach because that is the story of Spice Girls. Thus, the object of this study was Spice Girls’ song lyrics “Goodbye” in the form of lines and sentences. The detailed meaning of the song lyrics “Goodbye” tells about the parting between Spice Girls and X-member of Spice Girls “Gerry Haliwell”. She leaves Spice Girls because she wants to find out her own way to be a solo career. Although they are not together anymore but Spice Girls still love her and Gerry will always be in their heart. The song also describes about their togetherness in the past both in joy and sorrow. However, although they are not together anymore but Spice Girls will always help and support Gerry’s way. The general meaning of the song tells about the parting between Spice Girls and X-member of Spice Girls “Gerry Haliwell”. She has gone to leave them to find out her own way because she wants to be a solo career. The messages of the song lyrics “Goodbye” reminds us not to dissolve ourselves into the pain and never regret the parting because nothing is immortal in this life. Meeting and parting, joy and sorrow are the variation of this life and believe that inside the pain there must be lessons we can get

Generalized Sparse Covariance-based Estimation

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one grid-based method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem

In Memoriam: Daniel J. Meltzer

Sedan år 2006 har den syntetiskt framställda drogen spice existerat i Sverige, men först år 2008 blev drogen populär och tidningar började rikta uppmärksamhet mot den. Genom att drogen kan byta skepnad i uppbyggnaden kan den förbli laglig, därför kan egentligen namnet “spice” inte betraktas som ett enhetligt begrepp. Vårt syfte med denna studie blev att granska hur drogen spice beskrivs i tidningar och forskning. Även hur drogen betraktas gällande psykosociala och medicinska avseenden. Detta i förhållande till socialkonstruktivistiskt perspektiv. Den metod som vi valde att använda oss av i studien var kvantitativ innehållsanalys. Genom analys av 80 stycken svenska tidningsartiklar hämtade ur databasen mediearkivet, samt vetenskapliga artiklar och litteratur har vi besvarat våra frågeställningar. De resultat vi fick från analyser visade på att tidningar kan vara av betydande roll för ungdomars attityder. Tidningar kan utföra bland annat skrämselpropaganda för att upplysa och förhindra brukandet av spice, dessvärre visar resultatet en motsatt effekt. Forskning visar att bruk av spice kan påverka relationer och arbete negativt. Dessutom är några bieffekter av spice bröstsmärtor, vanföreställningar, självmordstankar och hjärtstopp