We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call ‘extender’ and ‘hypershallow’ graph sequences, respectively. Our main result is a probabilistic construction of non-hypershallow graph sequences.

This paper establishes a conjecture of Steel [7] regarding the structure of elementary embeddings from a level of the cumulative hierarchy into itself. Steel’s question is related to the Mitchell order on these embeddings, studied in [5] and [7]. Although this order is known to be illfounded, Steel conjectured that it has certain large wellfounded suborders, which is what we establish. The proof relies on a simple and general analysis of the much broader class of extender embeddings and a variant of the Mitchell order called the internal relation.

Field and laboratory experiments were conducted in 1983 and 1984 to compare the degradation of dichlormid (2,2-dichloro-N,N-di-2-prophenylacetamide), dietholate (O,O-diethyl O-phenylphosphorothioate), EPTC (S-ethyl dipropyl carbamothioate), and butylate [S-ethyl bis(2-methylpropyl) carbamothioate] in soils that had or had not been previously treated with each chemical. EPTC + dichlormid, butylate + dichlormid, EPTC + dichlormid + dietholate, or butylate + dichlormid + dietholate were applied annually for 4 yr to field plots to establish treatment histories. Butylate and EPTC degradation was enhanced in soils with previous histories of butylate and EPTC, respectively. Degradation rates of dietholate were equivalent in untreated soils or soils previously treated with EPTC + dietholate or butylate + dietholate.

Laboratory and field studies were conducted to examine the influence of R-33865 (O, O-diethyl-O-phenol phosphorothioate) on the degradation rate of EPTC (S-ethyl dipropylthiocarbamate) in three soils that had a history of repeated EPTC application and exhibited accelerated degradation of EPTC. In field studies, addition of R-33865 to EPTC extended EPTC persistence in soil and provided increased shattercane [Sorghum bicolor (L.) Moench] control. In two soils that exhibited rapid EPTC degradation, addition of R-33865 to EPTC extended the half-life of EPTC from 9 to 18 days and from 6 to 15 days, respectively. Evolution of 14CO2 from 14C-carbonyl EPTC-treated soils with a prior history of EPTC treatment was significantly reduced when R-33865 was added; however, the initial lag period of EPTC degradation was not restored. Addition of R-33865 to EPTC on soils with no prior EPTC treatment did not extend persistence of EPTC in soil.

In pig production, artificial insemination is widely carried out and the use of fresh diluted semen is predominant. For this reason, there are increasing interests in developing new extenders and in establishing the optimal storage conditions for diluted spermatozoa. In the last few decades, we utilised a homemade diluent (swine fertilisation medium (SFM)) for spermatozoa manipulation and biotechnological application as the production of transgenic pigs utilising the sperm-mediated gene transfer technique. The purpose of the present study is therefore to analyse the ability of SFM, in comparison to four commercial extenders, in preserving the quality of diluted boar semen stored at 16.5°C till 15 days. We utilised some of the main predictive tests as objectively measured motility, acrosome and sperm membrane integrity, high mitochondrial membrane potential and pH. Based on our in vitro study, SFM could be declared as a good long-term extender, able to preserve spermatozoa quality as well as Androhep Enduraguard for up to 6 to 9 days and more.

We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2κ = κ+n together with 2λ = λ+n for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible.

When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2λ = λ+n for all cardinals λ.

Mobile robotic manipulators can augment the strength and dexterity of human operators in unstructured environments. Here, the control system for a six degree-of-freedom heavy-lift mobile manipulator for lifting and inserting payloads on the deck of a ship is described. The robotic hardware and the application present several control challenges, including structural resonances, high joint friction that varies with time, limited sensors for measuring the joint friction, complex interaction with the environment, tight tolerances for the insertion tasks, lack of bilateral force feedback of the contact forces, and ship motions. The control system enables an operator to perform insertion tasks using feedback of tactile clues of the manipulator position, and reduces the effects of friction with a combination of sensor-based, adaptive, and model-based methods of friction compensation. The control architecture is validated in simulation and on a laboratory manipulator.