In 1975 Bollobás, Erdős, and Szemerédi asked the following question: given positive integers $n, t, r$ with $2\le t\le r-1$, what is the largest minimum degree $\delta (G)$ among all $r$-partite graphs $G$ with parts of size $n$ and which do not contain a copy of $K_{t+1}$? The $r=t+1$ case has attracted a lot of attention and was fully resolved by Haxell and Szabó, and Szabó and Tardos in 2006. In this article, we investigate the $r\gt t+1$ case of the problem, which has remained dormant for over 40 years. We resolve the problem exactly in the case when $r \equiv -1 \pmod{t}$, and up to an additive constant for many other cases, including when $r \geq (3t-1)(t-1)$. Our approach utilizes a connection to the related problem of determining the maximum of the minimum degrees among the family of balanced $r$-partite $rn$-vertex graphs of chromatic number at most $t$.

The interaction between product market competition, R&D investment, and the financing choices of R&D-intensive firms on the development of innovative products is only partially understood. We hypothesize that as competition increases, R&D-intensive firms will: i) increase R&D investment relative to existing assets in place; ii) carry more cash; and iii) maintain less net debt. Using the Hatch–Waxman Act as an exogenous shock to competition, we provide causal evidence supporting these hypotheses through a differences-in-differences analysis that exploits differences between the biopharma industry and other industries, and heterogeneity within the biopharma industry. We also explore how these changes affect innovative output.

Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K − 4 denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2−1 contains a K − 4-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markström [15] for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft [11] concerning almost perfect matchings in hypergraphs.

We describe observations with the Mopra radiotelescope designed to assess the feasibility of the H2O Maser Southern Galactic Plane Survey. We mapped two one-square-degree regions along the Galactic plane using the new 12-mm receiver and the UNSW Mopra spectrometer. We covered the entire spectrum between 19.5 and 27.5 GHz using this setup with the main aim of finding out which spectral lines can be detected with a quick mapping survey. We report on detected emission from H2O masers, NH3 inversion transitions (1,1), (2,2) and (3,3), HC3N (3–2), as well as several radio recombination lines.

A survey of the Milky Way disk and the Magellanic System at the wavelengths of the 21-cm atomic hydrogen (H i) line and three 18-cm lines of the OH molecule will be carried out with the Australian Square Kilometre Array Pathfinder telescope. The survey will study the distribution of H i emission and absorption with unprecedented angular and velocity resolution, as well as molecular line thermal emission, absorption, and maser lines. The area to be covered includes the Galactic plane (|b| < 10°) at all declinations south of δ = +40°, spanning longitudes 167° through 360°to 79° at b = 0°, plus the entire area of the Magellanic Stream and Clouds, a total of 13 020 deg2. The brightness temperature sensitivity will be very good, typically σT≃ 1 K at resolution 30 arcsec and 1 km s−1. The survey has a wide spectrum of scientific goals, from studies of galaxy evolution to star formation, with particular contributions to understanding stellar wind kinematics, the thermal phases of the interstellar medium, the interaction between gas in the disk and halo, and the dynamical and thermal states of gas at various positions along the Magellanic Stream.

This paper considers the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear stochastic differential equations of the generalized Itô type (containing both jump and diffusion components). We derive a particular functional partial differential equation which characterizes the exact likelihood function of a discretely sampled Itô process. In addition, we show by a simple counterexample that the common approach of estimating parameters of an Itô process by applying maximum likelihood to a discretization of the stochastic differential equation does not yield consistent estimators.

Objectives: We aimed to conduct a retrospective analysis of patients treated with radiotherapy for laryngeal carcinoma at a single institution.

Methods: We analysed data from 202 consecutive patients treated with primary or post-operative radiotherapy for laryngeal carcinoma over a 10-year period.

Results: Sixty-nine patients had a T1, 65 a T2, 39 a T3 and 29 a T4 lesion. Forty-one patients were node-positive. The clinical stage was I in 67 patients, II in 53, III in 36 and IV in 46. Primary radiotherapy was given to 152 patients. The median follow up was 60 months. The five-year overall local control rate was 86 per cent, the ultimate local control rate was 93 per cent, the five-year regional control rate was 96 per cent, the five-year relapse-free survival rate was 82 per cent and the five-year overall survival rate was 69 per cent.

Conclusions: Patients with laryngeal carcinoma treated with primary or post-operative radiotherapy had a five-year overall survival rate of 69 per cent.