With wide-field phased array feed technology, the Australian Square Kilometre Array Pathfinder (ASKAP) is ideally suited to search for seemingly rare radio transient sources that are difficult to discover previous-generation narrow-field telescopes. The Commensal Real-time ASKAP Fast Transient (CRAFT) Survey Science Project has developed instrumentation to continuously search for fast radio transients (duration $\lesssim$ 1 s) with ASKAP, with a particular focus on finding and localising fast radio bursts (FRBs). Since 2018, the CRAFT survey has been searching for FRBs and other fast transients by incoherently adding the intensities received by individual ASKAP antennas, and then correcting for the impact of frequency dispersion on these short-duration signals in the resultant incoherent sum (ICS) in real time. This low-latency detection enables the triggering of voltage buffers, which facilitates the localisation of the transient source and the study of spectro-polarimetric properties at high time resolution. Here we report the sample of 43 FRBs discovered in this CRAFT/ICS survey to date. This includes 22 FRBs that had not previously been reported: 16 FRBs localised by ASKAP to $\lesssim 1$ arcsec and 6 FRBs localised to $\sim 10$ arcmin. Of the new arcsecond-localised FRBs, we have identified and characterised host galaxies (and measured redshifts) for 11. The median of all 30 measured host redshifts from the survey to date is $z=0.23$. We summarise results from the searches, in particular those contributing to our understanding of the burst progenitors and emission mechanisms, and on the use of bursts as probes of intervening media. We conclude by foreshadowing future FRB surveys with ASKAP using a coherent detection system that is currently being commissioned. This will increase the burst detection rate by a factor of approximately ten and also the distance to which ASKAP can localise FRBs.

Seasonal influenza virus epidemics have a major impact on healthcare systems. Data on population susceptibility to emerging influenza virus strains during the interepidemic period can guide planning for resource allocation of an upcoming influenza season. This study sought to assess the population susceptibility to representative emerging influenza virus strains collected during the interepidemic period. The microneutralisation antibody titers (MN titers) of a human serum panel against representative emerging influenza strains collected during the interepidemic period before the 2018/2019 winter influenza season (H1N1-inter and H3N2-inter) were compared with those against influenza strains representative of previous epidemics (H1N1-pre and H3N2-pre). A multifaceted approach, incorporating both genetic and antigenic data, was used in selecting these representative influenza virus strains for the MN assay. A significantly higher proportion of individuals had a ⩾four-fold reduction in MN titers between H1N1-inter and H1N1-pre than that between H3N2-inter and H3N2-pre (28.5% (127/445) vs. 4.9% (22/445), P < 0.001). The geometric mean titer (GMT) of H1N1-inter was significantly lower than that of H1N1-pre (381 (95% CI 339–428) vs. 713 (95% CI 641–792), P < 0.001), while there was no significant difference in the GMT between H3N2-inter and H3N2-pre. Since A(H1N1) predominated the 2018–2019 winter influenza epidemic, our results corroborated the epidemic subtype.

Malaysia introduced graphic health warning labels (GHWLs) on all tobacco packages in 2009. We aimed to examine if implementing GHWLs led to stronger warning reactions (e.g., thinking about the health risks of smoking) and an increase in subsequent quitting activities; and to examine how reactions changed over time since the implementation of the GHWLs in Malaysia and Thailand where GHWL size increased from 50–55% in 2010. Data came from six waves (2005–2014) of the International Tobacco Control Southeast Asia Survey. Between 3,706 and 4,422 smokers were interviewed across these two countries at each survey wave. Measures included salience of warnings, cognitive responses (i.e., thinking about the health risks and being more likely to quit smoking), forgoing cigarettes, and avoiding warnings. The main outcome was subsequent quit attempts. Following the implementation of GHWLs in Malaysia, reactions increased, in some cases to levels similar to the larger Thai warnings, but declined over time. In Thailand, reactions increased following implementation, with no decline for several years, and no clear effect of the small increase in warning size. Reactions, mainly cognitive responses, were consistently predictive of quit attempts in Thailand, but this was only consistently so in Malaysia after the change to GHWLs. In conclusion, GHWLs are responded to more frequently, and generate more quit attempts, but warning wear-out is not consistent in these two countries, perhaps due to differences in other tobacco control efforts.

During the surveillance of influenza pandemics, underreported data are a public health challenge that complicates the understanding of pandemic threats and can undermine mitigation efforts. We propose a method to estimate incidence reporting rates at early stages of new influenza pandemics using 2009 pandemic H1N1 as an example. Routine surveillance data and statistics of travellers arriving from Mexico were used. Our method incorporates changes in reporting rates such as linearly increasing trends due to the enhanced surveillance. From our results, the reporting rate was estimated at 0·46% during early stages of the pandemic in Mexico. We estimated cumulative incidence in the Mexican population to be 0·7% compared to 0·003% reported by officials in Mexico at the end of April. This method could be useful in estimation of actual cases during new influenza pandemics for policy makers to better determine appropriate control measures.

The purpose of the present note is to answer the following question of T. A. Gillespie,learned from G. J. Murphy [4]: for which sequences{an} of complex numbers does there exist a quasinilpotent operator Q on a (separable, infinite-dimensional, complex) Hilbert space H, which has{an} as a diagonal, that is (Qen,en)=n for some orthonormal basis{en} in H?

The purpose of this paper is to answer the question: which self-adjoint operators on a separable Hilbert space are the real parts of quasi-nilpotent operators? In the finite-dimensional case the answer is: self-adjoint operators with trace zero. In the infinite dimensional case, we show that a self-adjoint operator is the real part of a quasi-nilpotent operator if and only if the convex hull of its essential spectrum contains zero. We begin by considering the finite dimensional case.

The choice of surrogate for plutonium oxide for use during the initial stages of research into the immobilization of intermediate level pyrochemical wastes containing plutonium andamericium oxides in a calcium phosphate host has been investigated by powder X-ray diffraction and X-ray absorption spectroscopy. Two non-radioactive surrogates, hafnium oxide and cerium oxide, together with radioactive thorium oxide were compared. Similarities in behaviour were observed for all three surrogates when calcined at the lowest temperature, 750°C but differences became more pronounced as the calcination temperature was increased to 950°C. Although some reaction occurred between all the surrogates and the host to form a substituted whitlockite phase, increasing the temperature led to a significant increase in the cerium reaction and the formation of an additional phase, monazite. Additionally it was observed that the cerium became increasingly trivalent at higher temperatures.

Low-frequency noise is investigated in n-type GaN film grown by rf-plasma assisted molecular beam epitaxy. The temperature dependence of the voltage noise power spectra, S V (f), was examined from 400K to 80K in the frequency range between 30Hz and 100KHz, which can be modeled as the superposition of 1/f (flicker) noise G-R noise. At f > 500 Hz the noise is dominated by G-R noise with activation energies of 360meV and 65meV from the conduct band. The results clearly demonstrate the trap origin for both the 1/f noise and G-R noise. At the low-frequency range the fluctuation was dominated by 1/f noise. To determine the origin of the noise we considered both the bulk mobility fluctuation and the trap fluctuation models. Our experimental results showed that rapid thermal annealing (RTA) at 800°C resulted in over one order of magnitude decrease in the Hooge parameter. Annealing at temperatures in excess of 1000°C resulted in significant increase in the noise. Photoluminescence and x-ray diffraction measurements also showed that the crystallinity of the films improved with RTA at 800°C with an accompanying reduction in deep levels. Annealing at 900°C and 1000°C resulted in an increase in the FWHM of the x-ray diffraction indicative of thermal decomposition of the materials. The results are in excellent agreement with the trend of Hooge parameters as a function of annealing temperature, strongly indicating trap origin of the observed 1/f noise.

Aluminum nitride (AlN) and gallium nitride (GaN) thin films have potential uses in high temperature, high frequency (e.g. microwave) acoustic devices. In this work, the piezoelectric coefficients of wurtzite AlN and GaN/AlN composite film grown on silicon substrates by molecular beam epitaxy were measured by a Mach-Zehnder type heterodyne interferometer. The effects of the substrate on the measured coefficients are discussed.

The result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DB C0(H) ⊆ DAL(H) if and only if DB C1(H) ⊆ DA L(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is the ideal of finite rank operators. 2. (Due to Fialkow [3]) For A, B ∊ L(H), we write T(A, B) for the map on L(H) sending S to AS - SB. Then the range of T(A, B)is the whole L(H) if it includes all finite rank operators L(H).

For a (bounded, linear) operator A in a (complex, infinite-dimensional, separable) Hilbert space ℋ, the inner derivation DA as an operator on ℬ(ℋ), is defined by DAX = AX – XA. Johnson and Williams [4] showed that, when A is a normal operator, range inclusion DBℬ(ℋ)⊆DA(ℋ)⊆ is equivalent to the condition that B = f(A), where f is a Lipschitz function on σ(A) such that t(z, w)(f(z)–f(w))/(z–w) is a trace class kernel on L2(μ) whenever t(z, w) is such a kernel. (Here μ is the dominating scalar valued spectral measure of A constructed in multiplicity theory). This result is deep and its proof is difficult. In the present paper, we establish the following analogous result which is easier to prove: for a normal operator A, range inclusion DB℘2(ℋ) holds if and only if B = f(A) for some Lipschitz function f on σ(A). Here ℘(ℋ) stands for the Hilbert-Schmidt class of operators on ℋ. As by-products of our argument, we generalize some results in [4], [8], [9] concerning the non-existence of a one-sided ideal contained in certain derivation ranges; for example, we show that if A is hyponormal and if the point spectrum σP(A*) of A* is empty, then DAℬ(ℋ) does not contain any nonzero right ideal.

It is proved that a bounded operator on Hilbert space is the sum of two quasi-nilpotent operators if and only if it is not a non-zero scalar plus a compact operator. Necessary conditions and sufficient conditions for an operator to be the product of two quasi-nilpotent operators are given.

1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius

1

of a Hilbert space operator T. Among the many interesting developments, we may mention:

(a) C. Berger's proof of the “power inequality”

2

(b) R. Bouldin's result that

3

for any isometry V commuting with T;

(c) the unification by B. Sz.-Nagy and C. Foias, in their theory of ρ-dilations, of the Berger dilation for T with w(T) ≤ 1 and the earlier theory of strong unitary dilations (Nagy-dilations) for norm contractions;

(d) the result by T. Ando and K. Nishio that the operator radii wρ (T) corresponding to the ρ-dilations of (c) are log-convex functions of ρ.

Let A be a complex Banach algebra with unit 1 satisfying ‖1‖ = 1. An element u in A is said to be unitary if it is invertible and ‖u‖ = ‖u−1‖ = 1. An element h in A is said to be hermitian if ‖exp(ifh)‖ = 1 for all real t; that is, exp(ith) is unitary for all real t. Suppose that J is a closed two-sided ideal and π: A → A/J is the quotient mapping. It is easy to see that if x in A is hermitian (resp. unitary), then so is π (x) in A/J. We consider the following general question which is the converse of the above statement: given a hermitian (resp. unitary) element y in A/J, can we find a hermitian (resp. unitary) element x in A such that π(x) = y? (The author has learned that this question, in a more restrictive form, was raised by F. F. Bonsall and that some special cases were investigated; see [1], [2].) In the present note, we give a partial answer to this question under the assumption that A is finite dimensional.

Let A be a complex Banach algebra with unit 1 satisfying ∥1∥ = 1. An element u in A is said to be unitary if it is invertible and ∥u∥ = ∥u−1∥ = 1. An element h in A is said to be hermitian if ∥exp(ith)∥ = 1 for all real t; that is, exp(ith) is unitary for all real t. Suppose that J is a closed two-sided ideal and π: A → A/J is the quotient mapping. It is easy to see that if x in A is hermitian (resp. unitary), then so is π(x) in A/J. We consider the following general question which is the converse of the above statement: given a hermitian (resp. unitary) element y in A/J, can we find a hermitian (resp. unitary) element x in A such that π(x)=y? (The author has learned that this question, in a more restrictive form, was raised by F. F. Bonsall and that some special cases were investigated; see [1], [2].) In the present note, we give a partial answer to this question under the assumption that A is finite dimensional.

Let Aj and Bj (1 ≦ j ≦ m) be bounded operators on a Banach space ᚕ and let Φ be the mapping on , the algebra of bounded operators on ᚕ, defined by

(1)

We give necessary and sufficient conditions for Φ to be identically zero or to be a compact map or (in the Hilbert space case) for the induced mapping on the Calkin algebra to be identically zero. These results are then used to obtain some results about inner derivations and, more generally, about mappings of the form

For example, it is shown that the commutant of the range of C(S, T) is “small” unless S and T are scalars.