We present an observational survey program using planetary nebulae, globular clusters, and X-ray emission to probe the halos of early-type galaxies. We review evidence for scanty dark matter halos around ordinary elliptical galaxies, and discuss the possible implications. We also present measurements of rotation in the halos.

Aaron J. Romanowsky

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.

Josef Dick

In the paper it is shown that there exist a function g from L1[0,1] and a weight function 0<u(x)<=1, so that g is universal for each classes L^p_u[0,1], p>= 1 with respect to signs-subseries of its Fourier-Walsh series.

Martin Grigoryan Tigran Grigoryan Artsrun Sargsyan

A 5'x5' region encompassing NGC6334I and I(N) has been mapped at a wavelength of 3mm (from 83.5 to 115.5GHz) with the Mopra telescope at an angular resolution between 33 arcsec and 36 arcsec. This investigation has made use of the recently installed 3mm MMIC receiver and the Mopra Spectrometer (MOPS) with broadband capabilities permitting total coverage of the entire frequency range with just five different observations. In total, the spatial distribution of nineteen different molecules, ions and radicals, along with additional selected isotopologues have been studied. Whilst most species trace the sites of star formation, CH_3CN appears to be most closely associated with NGC6334I and I(N). Both CN and C_2H appear to be widespread, tracing gas that is not associated with active star formation. Both N_2H^+ and HC_3N closely resemble dust continuum emission, showing they are reliable tracers of dense material, as well as the youngest stages of high mass star formation. Hot (E_u/k>100K) thermal CH_3OH emission is preferentially found towards NGC6334I, contrasting with I(N), where only cold (E_u/k<22K) thermal CH_3OH emission is found.

A. J. Walsh S. Thorwirth H. Beuther M. G. Burton

The T2K experiment is a long-baseline neutrino oscillation experiment which uses $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ beams to constrain CP-violating effects in a 3-flavor PMNS neutrino mixing model. Through $\nu_{\mu}\to\nu_{e}$ and $\bar{\nu}_{\mu}\to\bar{\nu}_{e}$ appearance channels, T2K is sensitive to CP-violating effects in neutrino mixing. An excess of $\nu_{e}$ candidates in the $\nu$-beam mode is observed when compared to the CP conserving cases. T2K finds a best fit value of $\delta_{\mathrm{CP}}=-1.97_{-0.70}^{+0.97}$ using Feldman-Cousins corrected intervals and excludes CP-conserving values of $\delta_{\mathrm{CP}}$ of $0$ and $\pi$ at the 90% CL. $J_{\mathrm{CP}}=0$ is also excluded at 2$\sigma$ when using a flat prior in $\delta_{\mathrm{CP}}$, favoring negative values.

J. G. Walsh

SDO-FM is a foundation model using data from NASA's Solar Dynamics Observatory (SDO) spacecraft; integrating three separate instruments to encapsulate the Sun's complex physical interactions into a multi-modal embedding space. This model can be used to streamline scientific investigations involving SDO by making the enormous datasets more computationally accessible for heliophysics research and enable investigations that require instrument fusion. We discuss four key components: an ingestion pipeline to create machine learning ready datasets, the model architecture and training approach, resultant embeddings and fine-tunable models, and finally downstream fine-tuned applications. A key component of this effort has been to include subject matter specialists at each stage of development; reviewing the scientific value and providing guidance for model architecture, dataset, and training paradigm decisions. This paper marks release of our pretrained models and embedding datasets, available to the community on Hugging Face and sdofm.org.

James Walsh Daniel G. Gass Raul Ramos Pollan Paul J. Wright Richard Galvez Noah Kasmanoff Jason Naradowsky Anne Spalding James Parr Atılım Güneş Baydin

In this PhD thesis we are dealing with convergence and summability of partial sums, Fej\'er and Marcinkiewicz means with respect to one- and two-dimensional Walsh-Fourier series on the martingale Hardy spaces. This thesis is focus to achieve the following main results: To find estimation of convergence and divergence of the subsequences of partial sums of the one-dimensional Walsh-Fourier series on the martingale Hardy spaces $H_p(G)$, when $0<p\leq1$. To find necessary and sufficient conditions in terms of modulus of continuity of martingale Hardy spaces, for which subsequences of partial sums of the one-dimensional Walsh-Fourier series convergence in $H_p(G)$ norm, when $0<p\leq1$. To find estimation of convergence and divergence of the subsequences of Fej\'er means of the one-dimensional Walsh-Fourier series on the martingale Hardy spaces $H_p(G)$, when $0<p\leq1/2$. To find necessary and sufficient conditions in terms of modulus of continuity of martingale Hardy spaces, for which subsequences of Fej\'er means of the one-dimensional Walsh-Fourier series converge in $H_{p}(G)$ norm, when $0<p\leq1/2$. To prove strong convergence of one-dimensional Fej\'er means with respect to Walsh system on the martingale Hardy spaces $H_{p}(G)$, when $0<p\leq 1/2$. To prove strong convergence of diagonal partial sums with respect to the two-dimensional Walsh-Fourier series on the martingale Hardy spaces $H_{p}(G^2)$, when $0<p<1$. To prove strong convergence of Marcinkiewicz means with respect to the two-dimensional Walsh-Fourier series in $H_{2/3}(G^2)$ norm. To find necessary and sufficient conditions in terms of modulus of continuity of Hardy spaces, for which Marcinkiewicz means of the two-dimensional Walsh-Fourier series converge in $H_{2/3}(G^2)$ norm.

George Tephnadze

In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin-Fourier (Walsh-Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh-Fourier series.

D. Lukkassen L. E. Persson G. Tephnadze G. Tutberidze

The detection and first identification of the deuterium Balmer emission lines, D-alpha and D-beta, in the core of the Orion Nebula is reported. Observations were conducted at the 3.6m Canada-France-Hawaii Telescope, using the Echelle spectrograph Gecko. These lines are very narrow and have identical 11 km/s velocity shifts with respect to H-alpha and H-beta. They are probably excited by UV continuum fluorescence from the Lyman (DI) lines and arise from the interface between the HII region and the molecular cloud.

G. Hebrard D. Pequignot A. Vidal-Madjar J. R. Walsh R. Ferlet

This review is focussed on the outer halos of elliptical galaxies. Its emphasis is on (i) planetary nebulae as test particles to trace the stellar kinematics at large radii, (ii) the observed angular momentum in elliptical galaxy halos and its theoretical relevance, (iii) dynamical modelling of stellar-kinematic data, and (iv) a discussion of the evidence for dark matter halos in ellipticals from a wide range of measurements.

Ortwin Gerhard