Operators in pre-Riesz spaces: moduli and homomorphisms

We focus on two topics that are related to moduli of elements in partially ordered vector spaces. First, we relate operators that preserve moduli to generalized notions of lattice homomorphisms, such as Riesz homomorphisms, Riesz* homomorphisms, and positive disjointness preserving operators. We also consider complete Riesz homomorphisms, which generalize order continuous lattice homomorphisms. Second, we characterize elements with a modulus by means of disjoint elements and apply this result to obtain moduli of functionals and operators in various settings. On spaces of continuous functions, we identify those differences of Riesz* homomorphisms that have a modulus. Many of our results for pre-Riesz spaces of continuous functions lead to results on order unit spaces, where the functional representation is used.

Microstructure and Mechanical Properties of Welded Joints in Austenitic Steel TP347HFG after Operation

The analysis involved a similar welded joint made of steel TP347HFG after operation at a temperature of 580°C. Tests revealed that the primary mechanisms responsible for the degradation of the microstructure in all areas of the joint subjected to analysis were precipitation processes within the grains and along the grain boundaries. The grain boundaries contained two morphologies forming a continuous lattice. Precipitation processes resulted in the high tensile strength of the joint and high hardness within the weld face area. After operation, the test joint was characterised by relatively high impact energy, which could be attributed to the fine-grained microstructure and the presence of numerous annealing twins.

New structural model of a chiral cubic liquid crystalline phase

A new model of a chiral cubic phase is proposed, in which the continuous lattice is embedded on a WP minimal primitive surface and chirality is related to the alternating inclination of molecules in the neighbouring segments of non-flat hexagons.

Coura and Valença Bridges on Minho Railway line – old structures, updated performance

<p>The pleasant Minho railway single lane line section from Caminha to Valença crosses the Minho river at Valença, through a very interesting and beautiful steel bridge. At Caminha it crosses the river Coura, by an also attractive steel bridge. Both are more than a century old and were refurbished and upgraded in a recent past and had before severe speed restrictions and load limitations:</p><ol><li> <p>Coura bridge: This 1879 iron bridge is a 3 span 164m lower deck continuous closed lattice girder, for a live load of only 4t/m without dynamic effects allowance. It was totally supported by a new continuous steel arch bridge, so both work together, combining in a very elegant construction.</p></li><li> <p>Valença bridge: This double-deck 1886 bridge is a steel 5 span 333m continuous lattice girder. Pathologies like excessive bending on the columns top sections, changing inappropriate bearing and a lock-up system for the braking action resulted in a demanding but discrete reinforcement.</p></li></ol>

Some operators and dimensions in modular meet-continuous lattices

Given a complete modular meet-continuous lattice [Formula: see text], an inflator on [Formula: see text] is a monotone function [Formula: see text] such that [Formula: see text] for all [Formula: see text]. If [Formula: see text] is the set of all inflators on [Formula: see text], then [Formula: see text] is a complete lattice. Motivated by preradical theory, we introduce two operators, the totalizer and the equalizer. We obtain some properties of these operators and see how they are related to the structure of the lattice [Formula: see text] and with the concept of dimension.