Evidence of the relationship between fecal short-chain fatty acids (SCFA) levels, dietary quality and type 2 diabetes mellitus (T2DM) in rural populations is limited. Here, we aimed to investigate the association between fecal SCFA levels and T2DM and the combined effects of dietar quality on T2DM in rural China. In total, 100 adults were included in the case–control study. Dietary quality was assessed by the Alternate Healthy Eating Index 2010 (AHEI-2010), and SCFA levels were analysed using the GC-MS system. Generalised linear regression was conducted to calculate the OR and 95 % CI to evaluate the effect of SCFA level and dietary quality on the risk of T2DM. Finally, an interaction was used to study the combined effect of SCFA levels and AHEI-2010 scores on T2DM. T2DM participants had lower levels of acetic and butyric acid. Generalised linear regression analysis revealed that the OR (95 % CI) of the highest acetic and butyric acid levels were 0·099 (0·022, 0·441) and 0·210 (0·057, 0·774), respectively, compared with the subjects with the lowest tertile of level. We also observed a significantly lower risk of T2DM with acetic acid levels > 1330·106 μg/g or butyric acid levels > 585·031 μg/g. Moreover, the risks of higher acetic and butyric acid levels of T2DM were 0·007 (95 % CI: 0·001, 0·148), 0·005 (95 % CI: 0·001, 0·120) compared with participants with lower AHEI-2010 scores (all P < 0·05). Acetate and butyrate levels may be important modifiable beneficial factors affecting T2DM in rural China. Improving dietary quality for body metabolism balance should be encouraged to promote good health.

To solve the problem of the leakage of phase-change materials and expand the application of clay minerals in the field of phase-change materials, illite and paraffin wax were used for the first time as a new binary hybrid core material with silica as the wall material. Phase-change microcapsules were prepared using the sol–gel method and successfully applied in silicone rubber foams. Differential scanning calorimetry showed that the microcapsules had a melting temperature of 62.99°C and a latent heat capacity of 98.24 J g–1, indicating their good heat-storage capacity. Furthermore, the effectiveness of using illite as a filler for preventing paraffin leakage was demonstrated through 200 thermal cycling tests, which demonstrated a leakage rate of only 2.6% compared to 3.2% exhibited by microcapsules without illite.

In this paper, we study carbon emission trading whose market is gaining in popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on CO2 emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

The main result established that the mapping V → V ∩ W (V ∈ ℒ(F)) is a complete endomorphism of the lattice ℒ(F) of pseudovarieties of finite semigroups for certain particular pseudovarieties W, including the pseudovariety of bands.