In this article, we set up some adequate conditions for analytic functions associated with cosine hyperbolic function. We determine conditions on α such that 1+α (ϰ^(2+P(j-1) ) g^' (ϰ))/(Pg^j (ϰ)),for each j=0,1,2,3 are subordinated by Janowski function, then (g(ϰ))/ϰ^P <cosℏ⁡(ϰ),(ϰ∈C). By choosing specific values of functions g we get some adequate conditions for multivalent starlike function related with cosine hyperbolic.

The Omicron EG.5 lineage of SARS-CoV-2 is currently on a trajectory to become a dominant strain. This phase 2 study aims to evaluate the immunogenicity of SCTV01E-2, a tetravalent protein vaccine, with a specific emphasis on its effectiveness against Omicron EG.5, comparing it with its progenitor vaccine, SCTV01E (NCT05933512). As of September 12, 2023, 429 participants aged ≥18 years were randomized to SCTV01E (N=215) or SCTV01E-2 (N=214) groups. Both vaccines showed increases in neutralizing antibody (nAb) against Omicron EG.5, with a 5.7-fold increase and a 9.0-fold increase in SCTV01E and SCTV01E-2 groups 14 days post-vaccination, respectively. The predetermined statistical endpoints were achieved, showing that the geometric mean titer (GMT) of nAb and the seroresponse rate (SRR) against Omicron EG.5 were significantly higher in the SCTV01E-2 group compared to SCTV01E. Additionally, SCTV01E and SCTV01E-2 induced a 5.5-fold and a 5.9-fold increase of nAb against XBB.1, respectively. Reactogenicity was generally mild and transient. No vaccine related SAEs, AESIs or deaths were reported. In summary, SCTV01E-2 elicited robust neutralizing responses against Omicron EG.5 and XBB.1 without safety concerns, underlining its potential as a versatile COVID-19 vaccine against SARS-CoV-2 variants.

Tough and antimicrobial dual-crosslinked poly((trimethylamino)ethyl methacrylate chloride)-phytic acid hydrogel (pTMAEMA-PA) has been synthesized by adding chemical crosslinker and docking physical crosslinker of multivalent phytic acid into a cationic polyelectrolyte network. By increasing the loading concentration of PA, the tough hydrogel exhibits compressive stress of >1 MPa, along with high elasticity and fatigue-resistant properties. The enhanced mechanical properties of pTMAEMA-PA were stem from multivalent ion effect of PA via the formation of ion bridges within polyelectrolytes. In addition, a comparative study for a series of pTMAEMA-counterion complexes was conducted to elaborate the relationship between swelling ratio and mechanical strength. The study also revealed secondary factors, such as ion valency, ion specificity and hydrogen bond formation, holding crucial roles in tuning mechanical properties of the polyelectrolyte hydrogel. Furthermore, in bacteria attachment and disk diffusion tests, pTMAEMA-PA exhibits superior fouling resistance and antibacterial capability. The results reflect the fact that PA enables chelating strongly with divalent metal ions, hence, disrupting the outer membrane of bacteria, as well as dysfunction of organelles, DNA and protein. Overall, the work demonstrated a novel strategy for preparation of tough polyelectrolyte with antibacterial capability via docking PA to open up the potential use of PA in medical application.