We study linear-quadratic optimal control problems for infinite-dimensional dissipative systems with possibly indefinite cost functionals, subject to the additional requirement that the state converges to zero as time tends to infinity. Assuming the existence of a bounded quadratic storage function and an appropriate state-feedback stabilizability condition, we show that the indefinite optimal control problem is equivalent to a linear-quadratic optimal control problem with a nonnegative cost functional. We establish the relationship between the corresponding value functions and derive the associated operator-node Lur'e equation. Finally, we illustrate the results by several examples. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Amongst the different techniques used for the production of coatings, magnetron sputtering (MS) has been efficiently used for the synthesis of functional metallic coatings of varying composition. However, the complex nature of the MS process has deemed the extraction of detailed mechanistic insight an experimentally challenging task, with the process design often being regulated by trials. Although several computational modelling methods have emerged in order to study the MS process in detail, they often focus on simple reactor geometries and process setups, with the deposition of multicomponent coatings often falling outside the scope of such studies. In this work, a computational, fluid-type model for the MS process design is developed, in order to study the different phenomena taking place within a complex reactor setup, with multiple targets and substrates. The computational approach is validated using experimental measurements from two independent studies in relevant published literature, yielding R2 values of 0.960 and 0.914, and NRMSE values of 0.083 and 0.099, respectively. Using the developed model, the key mechanisms and phenomena that dictate the process are analyzed, alongside the effect of several process conditions on the control of film growth, uniformity, as well as composition, for the case of multi-target deposition. The use of such models allows a more in-depth analysis of MS processes and reactors, thus paving the way towards a more knowledge-based process optimization and scale-up.
When environments change sequentially, past conditions can leave legacies that modify population growth and trait expression under subsequent stress. Under global change, sequences such as marine heatwaves followed by pollution runoff increase the likelihood and consequence of such legacies for population and community dynamics. We tested for sequence-dependent legacy effects in six globally distributed strains of the marine phytoplankton Synechococcus sp. using a full-factorial microcosm experiment with warming, herbicide pollution, and control treatments as both chronic (constant) and sequential (changing) exposures. We quantified chronic and acute sensitivities as changes in population density, per capita growth rate, cell size and chlorophyll content following respective exposures. Significant chronic sensitivity occurred in 58.3% of strain-exposure combinations and significant acute sensitivity in 48%; acute responses often showed decoupling between growth and traits. Comparisons of chronic and acute sensitivities demonstrate that past environments systematically alter subsequent responses, producing strain- and exposure-specific overcompensation or undercompensation. Consequently, incorporating sequence-based legacies into predictions of biodiversity dynamics and ecosystem function under global change is essential.
Delving into the persistent impacts of colonialism within the sphere of modern science, we explore some of the deep-seated disparities between the Global North and South with regards to the scientific enterprise. Central to this inequality are the hurdles of language and financial support. As such, this work discusses the often-overlooked obstacles that Global South scientists face, including the additional efforts non-native English speakers must invest in reading and publishing, their higher rejection rates, and the widespread neglect of publications in languages other than English. These challenges not only hinder the advancement of science but also deepen existing divides. Furthermore, we examine the double-edged sword of and the geopolitical limits of open science. While these policies democratize access to scientific knowledge, they can inadvertently exacerbate the North-South inequalities due to, for example, the prohibitive costs associated with open-access publishing-a financial burden that is often unmanageable for researchers with limited funding. This funding gap severely restricts the Global South's scientific capabilities and impact, affecting everything from conducting comprehensive research to attending scientific meetings. The culmination of these disparities not only diminishes the impact of Global South researchers in their fields but also traps them in a cycle of reduced funding and limited global networking opportunities. In addressing these complex issues, the contributions in this work highlight some of the most common and pronounced issues related to scientific inequalities, as well as suggesting possible ways of bridging these gaps in order to reach a more equitable distribution of resources and recognition in the global scientific community.
A novel imine-based ligand (E)-2-(4-(((2-hydroxynaphthalen-1-yl)methylene)amino)phenyl)acetonitrile was synthesized via mechanochemistry from 4-aminobenzylcyanide and 2-hydroxy-1-naphthaldehyde, achieving >99% yield. The ligand demonstrated exceptional Cu2+ ion sensing through colorimetric detection, with a rapid visual response and a low detection limit (4.7 & times; 10(-)(8) M). Structural studies revealed 2:1 (L-Cu-2(+)) complex formation, confirmed by Job's plot and H-1 NMR titration analyses. To enhance aqueous performance, host-guest complexation with beta-cyclodextrin was investigated. UV-Vis and NMR spectroscopy confirmed 1:1 inclusion complex formation (K-a = 6.2 & times; 10(5) M--(1)) through aminobenzyl cyanide insertion into the beta-CD cavity. The L-beta-CD system significantly improved selectivity by reducing Al-3(+) and Hg-2(+) interference while maintaining comparable sensitivity (LOD = 4.8 & times; 10(-)(8) M). Real-world validation showed superior recovery rates (94.2%-110.0%) compared to free ligand (87.2%-114.7%). Biomolecular interaction studies revealed moderate DNA intercalation (K-a = 1.2 & times;10(4) M--(1)) attenuated by beta-CD inclusion (K-a = 3.5 & times; 10(3) M--(1)), while bovine serum albumin (BSA) binding was slightly enhanced (K-a increased from 2.2 & times; 10(6) to 4.0 & times; 10(6) M--(1)). This represents the UV-Vis investigation of beta-cyclodextrin influence on Cu-2(+) sensing, providing insights for an advanced supramolecular analytical platform.
