Optimality conditions and constraint qualifications for cardinality constrained optimization problems

The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive subspaces constraints (MPDSC). Since a subspace is a special case of a convex polyhedral set, MPDSC is a special case of the mathematical program with disjunctive constraints (MPDC). Using the special structure of subspaces, we are able to obtain more precise formulas for the tangent and (directional) normal cones for the disjunctive set of subspaces. We then obtain first and second order optimality conditions by using the corresponding results from MPDC. Thanks to the special structure of the subspace, we are able to obtain some results for MPDSC that do not hold in general for MPDC. In particular we show that the relaxed constant positive linear dependence (RCPLD) is a sufficient condition for the metric subregularity/error bound property for MPDSC which is not true for MPDC in general. Finally we show that under all constraint qualifications presented in this paper, certain exact penalization holds for CCOP

Epidemiological Characteristics of Varicella under Different Immunisation Strategies in Suzhou Prefecture, Jiangsu Province

Background: The varicella vaccine is excluded from the Chinese national immunisation programme but is included in the local expanded programme on immunisation (EPI) in the Suzhou Prefecture. This study investigated the epidemiological characteristics of the varicella cases during the implementation of different immunisation strategies in the Suzhou Prefecture, Jiangsu Province. Methods: In this study, we used descriptive statistics. Information on reported instances from 2012 to 2021 was first retrieved. Data on varicella cases were collected from the China Information System for Disease Control and Prevention (CISDCP). Similarly, information on vaccinated children was obtained from the Jiangsu Province Vaccination Integrated Service Management Information System (JPVISMIS). The census data in this study was procured from the Suzhou Bureau of Statistics. Results: From 2012 to 2021, a total of 118,031 cases of varicella were reported in Suzhou, and the average annual reported incidence was 91.35 per 100,000. The average yearly incidence after implementing the two-dose varicella vaccination decreased by 41.57% compared with the implementation of one dose. This study demonstrates two annual incidence peaks, a small peak between April and July and a prominent peak between October and January. It is also possible that this seasonal distribution is related to the geography of Suzhou. The average annual reported incidence between districts with a statistically significant difference (χ2 = 98.077, p < 0.05). The one-dose varicella vaccination coverage gradually increased from 55.34% in 2012 to 89.06% in 2021 and the two-dose varicella vaccination coverage gradually increased from 0.27% in 2012 to 82.17% in 2021. Conclusions: Administering the varicella vaccine in the local EPI has significantly decreased the incidence rate and the total number of cases. A two-dose vaccination schedule is still the best vaccination strategy for varicella vaccine effectiveness

Short hydrogen-bond network confined on COF surfaces enables ultrahigh proton conductivity

The idea of spatial confinement has gained widespread interest in myriad applications. Especially, the confined short hydrogen-bond (SHB) network could afford an attractive opportunity to enable proton transfer in a nearly barrierless manner, but its practical implementation has been challenging. Herein, we report a SHB network confined on the surface of ionic covalent organic framework (COF) membranes decorated by densely and uniformly distributed hydrophilic ligands. Combined experimental and theoretical evidences have pointed to the confinement of water molecules allocated to each ligand, achieving the local enrichment of hydronium ions and the concomitant formation of SHBs in water-hydronium domains. These overlapped water-hydronium domains create an interconnected SHB network, which yields an unprecedented ultrahigh proton conductivity of 1389 mS cm(-1) at 90 degrees C, 100% relative humidity. When hydronium ions are enriched in confined water, short hydrogen bonds (SHBs) form due to the constrained space of excess protons between pairs of water molecules. Here authors demonstrate a SHB network confined on the surface of ionic COF membranes with tunable -SO3H groups, with proton conductivity of 1389 mS cm(-1) at 90 C-o

Short hydrogen-bond network confined on COF surfaces enables ultrahigh proton conductivity

The idea of spatial confinement has gained widespread interest in myriad applications. Especially, the confined short hydrogen-bond (SHB) network could afford an attractive opportunity to enable proton transfer in a nearly barrierless manner, but its practical implementation has been challenging. Herein, we report a SHB network confined on the surface of ionic covalent organic framework (COF) membranes decorated by densely and uniformly distributed hydrophilic ligands. Combined experimental and theoretical evidences have pointed to the confinement of water molecules allocated to each ligand, achieving the local enrichment of hydronium ions and the concomitant formation of SHBs in water-hydronium domains. These overlapped water-hydronium domains create an interconnected SHB network, which yields an unprecedented ultrahigh proton conductivity of 1389 mS cm(-1) at 90 degrees C, 100% relative humidity. When hydronium ions are enriched in confined water, short hydrogen bonds (SHBs) form due to the constrained space of excess protons between pairs of water molecules. Here authors demonstrate a SHB network confined on the surface of ionic COF membranes with tunable -SO3H groups, with proton conductivity of 1389 mS cm(-1) at 90 C-o