Global dynamics of a class of SEIRS epidemic models in a periodic environment

In this paper, we study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number R₀ which is defined through the spectral radius of a linear integral operator. If R₀<1, then the disease free periodic solution is globally asymptotically stable and if R₀>1, then the disease persists. Our results really improve the results in [T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology Bull. Math. Biol. 69 (8) (2007) 2537-2559] for the periodic case. Moreover, from our results, we see that the eradication policy on the basis of the basic reproduction number of the time-averaged system may overestimate the infectious risk of the periodic disease. Numerical simulations which support our theoretical analysis are also given.     

The thermal stability and related properties of iron-base glasses

The crystallization temperature of Fe_80?XM_XP₁₃C₇ and Fe_80?XN_XP₁₃C₇ alloys has been investigated, where M is Zr, Nb, Mo, Ru, Rh or Pd, and N is B, C, Si, P, As, Sn or Sb. Zr and Mo effectively increase T_X and Pd decreases it. The increase in crystallization temperature T_X with the concentration of elements M, is larger for the second group of periodic elements, except for the case of Pd, compared with the first group of periodic elements. The crystallization temperature is related to the average electron concentration, the atomic size and the atomic cohesive energy of the additive metal.The metalloidal elements N, except for Sn and Sb, increase the T_X of Fe_80?XN_XP₁₃C₇ alloys. In particular, the addition of B, C, Si of P definitely increases T_X and small amounts of Sn or Sb markedly decrease it. Contrary to the effects of metallic elements, the effects of metalloidal elements do not show the general trend. However, in the same group of the periodic system T_X decrease with increasing the atomic size and decreasing cohesive energies for metalloidal elements.     

Nucleophilic aromatic substitution using Et3SiH/cat. t-Bu-P4 as a system for nucleophile activation

A novel type of deprotonative arylation of nucleophiles was conducted using Et(3)SiH/cat. t-Bu-P4 and the powerful S(N)Ar reactions of aryl fluorides were accomplished using alcohols and malonates as nucleophiles.     

Simultaneous anomalous reflection and quartz-crystal microbalance measurements of protein bindings on a gold surface

Protein bindings onto a gold surface were detected simultaneously by QCM (delta F(water)) and anomalous reflection (deltaR) of gold on the same surface in aqueous solutions; the obtained delta F(water)/deltaR values correlated with surface areas and viscosity of proteins.     

Reverse photochromic behavior of an iron-magnesium complex

We have obtained a novel heterobimetallic iron-magnesium complex, (THF)4Mg(mu-Br)2FeBr2 (THF = tetrahydrofuran), which showed reverse photochromism in THF. The response exhibited in this system is associated with d-orbital splitting of the Fe atom and a change in the molecular aggregation state (dimerization).     

Synthesis of a star-shaped polymer via coordination of ester-linked pyridyl-terminated poly(oxyethylene) with ru(II)

The star-shaped polymer with trans-tetrapyridyl complex of Ru(II) as a core was prepared by complexation of ester-linked pyridyl-terminated poly(oxyethylene) (M̄_n = 2000) with a Ru₅Cl₁₂²⁻ cluster. The unimodal peak of the star-shaped polymer in the gel-permeation chromatogram was shifted to a higher molecular weight region than that of the starting prepolymer. The electron-withdrawing ester substituent in para position of the pyridine ring shifted the metal-to-ligand charge transfer (MLCT) band into the visible region.     

Polymers with double-decker and side-opened cage silsesquioxanes: Effects of cage structures on materials properties

Cage silsesquioxanes, also known as polyhedral oligomeric silsesquioxanes (POSS), serve as crucial building blocks in crafting precisely designed organic–inorganic hybrid materials, given that their well-defined silsesquioxane clusters can be adorned with organic substituents. While polymers with POSS in their main chains have been thoroughly examined, analyzing the correlation between cage structure and material properties in main-chain-type polymers remains challenging. This difficulty stems from the limited range of organic substituents on traditional POSS monomers, thereby precluding comparisons between polymers with unified substituents and different cage structures. In this study, we synthesized double-decker silsesquioxane (DDSQ) and side-opened POSS (SO-POSS) monomers, both featuring phenyl groups. Subsequent platinum-catalyzed hydrosilylation polymerization yielded main-chain-polymers. Both the cage and linker structures influence thermal stability and the glass transition temperature, while the hardness was primarily determined by the linker structure. This research is the first to elucidate the impact of cage structure on the material properties of main-chain-type POSS polymers.     

Effect of Flow Structures on Turbulence Statistics of Taylor-Couette Flow in the Torque Transition State

Direct numerical simulations of Taylor-Couette flow from Re= 8000 to 25000 have been conducted to investigate changes of turbulence statistics in the transition of the Reynolds number dependency of the mean torque near Re= 10000. The velocity fluctuations are decomposed into the contributions of the Taylor vortex and remaining turbulent fluctuations. Significant Reynolds number dependencies of these components are observed in the radial profiles of the Reynolds stress and the transmission of the mean torque. The contributions of Taylor vortex and turbulent components in the net amount of mean torque are evaluated. The Taylor vortex component is overtaken by the turbulent counterpart around Re= 15000 when they are defined as the azimuthally averaged component and the remnants. The results show that the torque transition can be explained by the competition between the contributions of azimuthally averaged Taylor vortex and the remaining turbulent components.     

Photorefractive effect in ferroelectric liquid crystals

In this paper, we review recent progress of research on the photorefractive effect of ferroelectric liquid crystals. The photorefractive effect is a phenomenon that forms a dynamic hologram in a material. The interference of two laser beams in a photorefractive material establishes a refractive index grating. This phenomenon is applicable to a wide range of devices related to diffraction optics including 3D displays, optical amplification, optical tomography, novelty filters, and phase conjugate wave generators. Ferroelectric liquid crystals are considered as a candidate for practical photorefractive materials. A refractive index grating formation time of 8–10 ms and a large gain coefficient are easily obtained in photorefractive ferroelectric liquid crystals.     

Synthesis of Block Copolymers with a Pentasilane Core

We report a new method for the synthesis of block copolymers with a pentasilane core by the polymerization of alkyl methacrylate monomers using the pentasilyl dianion as an initiator. The polymerization proceeded with living features and yielded the corresponding block copolymers with controlled molecular weights. The amphiphilic block copolymer was obtained by the polymer reaction, and it formed sphere‐like aggregates in MeOH/H₂O solution.