Weak compactness of almost limited operators

The paper is devoted to the relationship between almost limited operators and weakly compacts operators. We show that if $F$ is a $\sigma$-Dedekind complete Banach lattice then, every almost limited operator $T:E\rightarrow F$ is weakly compact if and only if $E$ is reflexive or the norm of $F$ is order continuous. Also, we show that if $E$ is a $\sigma$-Dedekind complete Banach lattice then the square of every positive almost limited operator $T:E\rightarrow E$ is weakly compact if and only if the norm of $E$ is order continuous.Comment: 5 page

A 2-Dimensional Cellular Automaton for Agents Moving from Origins to Destinations

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise ($p$) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter $"\mu"$ is also introduced to control the probability that the movement of all agents involved to the same site (conflict) is denied at one time step. This model displays two states; namely the freely moving and the jamming state. If $\mu$ is large and $p$ is low, the system is in the jamming state even if the density is low. However, if $\mu$ is large and $p$ is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if $\mu$ is large and $p$ is low (jamming state); but long travel times are suppressed if $p$ becomes large (freely moving state).Comment: 10 pages, 12 figure

Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians

It has been argued that it is incompatible to maintain unitary time evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a nonobservable operator as it ceases to be quasi-Hermitian when the metric becomes time dependent

Dynamic response studies on aggregation and breakage dynamics of colloidal dispersions in stirred tanks

Aggregation and breakage of aggregates of fully destabilized polystyrene latex particles in turbulent flow was studied experimentally in both batch and continuous stirred tanks using small-angle static light scattering. It was found that the steady-state values of the root-mean-square radius of gyration are fully reversible upon changes of stirring speed as well as solid volume fraction. Steady-state values of the root-mean-square radius of gyration were decreasing with decreasing solid volume fraction as well as with increasing stirring speed. Moreover, it was found that the steady-state structure and shape of the aggregates is not influenced by the applied stirring speed

An examination of UK companies' modern slavery disclosure practices: Does board gender diversity matter?

The United Nations' Sustainable Development Goals persuade governments and businesses to fight modern slavery as part of the 2030 Agenda for Sustainable Development. The UK government took the initiative by introducing the Modern Slavery Act in 2015. Despite this, little is known about how companies disclose information about their efforts to tackle modern slavery as required by the Act and the role of corporate governance as a determinant of modern slavery disclosure (MSD) levels. This study, therefore, investigates the extent to which companies engage in MSD and empirically examines the impact of board gender diversity (BGD) on MSD. Based on a content analysis of FTSE 100 companies' modern slavery statements during the 2016–2020 period, we find that MSD improved over time but is still relatively low. Our results show that companies pay less attention to the core practices of modern slavery, such as key performance indicators (KPIs), due diligence procedures, risk assessment and management, and training. This evidence suggests that companies tend to comply with the Act by focusing largely on symbolic structures rather than providing a comprehensive disclosure of their impacts on modern slavery practices to minimise regulatory risks and manage stakeholders' perceptions. We also find that boards with greater female representation have a positive and significant association with MSD. This finding is consistent with the gender socialisation theory in that women are more sensitive to communal values and ethics. Consequently, companies with a greater proportion of female directors are more transparent about their strategies and actions related to fighting modern slavery. Furthermore, a critical mass of at least four female directors is necessary before any positive impact on MSD can be observed. Our findings shed new light on this under-researched area and the role of female directors in addressing modern slavery risk and can be of interest to companies, policymakers, and other stakeholders