We describe the scientific goals and survey design of the First Large Absorption Survey in H i (FLASH), a wide field survey for 21-cm line absorption in neutral atomic hydrogen (H i) at intermediate cosmological redshifts. FLASH will be carried out with the Australian Square Kilometre Array Pathfinder (ASKAP) radio telescope and is planned to cover the sky south of $\delta \approx +40\,\deg$ at frequencies between 711.5 and 999.5 MHz. At redshifts between $z = 0.4$ and $1.0$ (look-back times of 4 – 8 Gyr), the H i content of the Universe has been poorly explored due to the difficulty of carrying out radio surveys for faint 21-cm line emission and, at ultra-violet wavelengths, space-borne searches for Damped Lyman- $\alpha$ absorption in quasar spectra. The ASKAP wide field of view and large spectral bandwidth, in combination with a radio-quiet site, will enable a search for absorption lines in the radio spectra of bright continuum sources over 80% of the sky. This survey is expected to detect at least several hundred intervening 21-cm absorbers and will produce an H i-absorption-selected catalogue of galaxies rich in cool, star-forming gas, some of which may be concealed from optical surveys. Likewise, at least several hundred associated 21-cm absorbers are expected to be detected within the host galaxies of radio sources at $0.4 < z < 1.0$ , providing valuable kinematical information for models of gas accretion and jet-driven feedback in radio-loud active galactic nuclei. FLASH will also detect OH 18-cm absorbers in diffuse molecular gas, megamaser OH emission, radio recombination lines, and stacked H i emission.

The Murchison Widefield Array (MWA) is an open access telescope dedicated to studying the low-frequency (80–300 MHz) southern sky. Since beginning operations in mid-2013, the MWA has opened a new observational window in the southern hemisphere enabling many science areas. The driving science objectives of the original design were to observe 21 cm radiation from the Epoch of Reionisation (EoR), explore the radio time domain, perform Galactic and extragalactic surveys, and monitor solar, heliospheric, and ionospheric phenomena. All together $60+$ programs recorded 20 000 h producing 146 papers to date. In 2016, the telescope underwent a major upgrade resulting in alternating compact and extended configurations. Other upgrades, including digital back-ends and a rapid-response triggering system, have been developed since the original array was commissioned. In this paper, we review the major results from the prior operation of the MWA and then discuss the new science paths enabled by the improved capabilities. We group these science opportunities by the four original science themes but also include ideas for directions outside these categories.

A new 7-beam methanol multibeam receiver is being used to survey the Galaxy for newly forming massive stars, that are pinpointed by strong methanol maser emission at 6.668 GHz. The receiver, jointly constructed by Jodrell Bank Observatory (JBO) and the Australia Telescope National Facility (ATNF), was successfully commissioned at Parkes in January 2006. The Parkes-Jodrell survey of the Milky Way for methanol masers is two orders of magnitude faster than previous systematic surveys using 30-m class dishes, and is the first systematic survey of the entire Galactic plane. The first 53 days of observations with the Parkes telescope have yielded 518 methanol sources, of which 218 are new discoveries. We present the survey methodology as well as preliminary results and analysis.

The second dual of the vector-valued function space C0(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodým property. As an application we present a simple proof that C0 (S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure μh is given, where , h ∈ L∞ (|μ;|, A**) and μh is defined by the Arens product.

Let Sbe a topological semigroup, K a compact convex subset of a separated convex space Eand T: S x K → K an affine action (denoted by (s, x) → Ts(x),s ∈ S, x ∈ K) of S as continuous affine maps on K. It is shown in A. Lau and J. Wong [22] that the weakly left uniformly measurable functions WLUM(S) on S has a left invariant mean iff Shas the fixed point property for weakly measurable affine actions, i.e. affine actions such that the scalar function s → x*Ts(x) is measurable for each x ∈ K and x*∈ E* (the dual of E) with respect to the Borel sets in S. It is natural to ask for a “strongly” measurable analogue of this result. There are a number of ways to define such actions and the corresponding functions on S. In this paper, we obtained a neat analogue of this fixed point theorem by a suitable choice of strong measurability which naturally leads to another new fixed point theorem for separable actions. Also, we shall unify these and many known fixed point theorems and extend and generalise them to anti-actions of S as bounded linear operators on Banach spaces

This is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.

In this paper, we prove that if S is a locally compact semigroup and T a locally compact Borel measurable subsemigroup of S, then T has a topological left invariant mean if and only if there is a topological left T-invariant mean M on S such that M(xT) = 1, where xT is the characteristic functional of T in S.

Let S be a locally compact semigroup and M(S) its measure algebra. It is shown that the dual M(S)* is isometrically order isomorphic to the space GL(S) of all generalised functions on S first introduced by Šreǐder (1950). Moreover, convolutions of elements in each of the spaces M(S)* and GL(S) can be defined in such a way that the above isomorphism preserves convolutions. These results on representation of functionals in M(S)* by generalised functions practically open up a new chapter in abstract harmonic analysis. As an example, some applications to invariant means on locally compact semigroups are given.

In this paper, we introduce the concept of topological left substantial subsemigroup of a locally compact semigroup S and prove that if T is such a subsemigroup in S and M(T) is the measure algebra of T, then M(T)* is topological left amenable iff M(S)* is topological left amenable, an extension of a similar result for discrete semigroups.

Let S be a locally compact Borel subsemigroup of a locally compact semigroup G. It is shown that the algebra of all "absolutely continuous' measures on S is isometrically order isomorphic to the algebra of all measures in M(G) which are "concentrated" and "absolutely continuous" on S.