Zn2+@Polyvinylpyrrolidone and Urushiol Preparation of Nanofibrous Membranes and Their Synergistic Effect

In this study, lacquer is gathered from a lacquer tree and rotary evaporation is used to remove impurities to obtain urushiol. Next, 10 mL of anhydrous ethanol serves as the solvent for blending polyvinylpyrrolidone (PVP) at a specified content (0.7 g and 0.2–0.7 g urushiol) to form an electrospinning solution. Electrospinning is carried out with a voltage of 18 kV to prepare PVP/urushiol nanofibrous membranes. At a ratio of 7/4, the PVP/urushiol nanofibrous membranes are not eroded in 98% sulfuric acid and these membranes also demonstrate a 50–60% antibacterial effect against Staphylococcus aureus and Escherichia coli. Moreover, the antibacterial effect can be boosted to 98% with the incorporation of zinc ions. The results indicate that anhydrous ethanol can remove the sensitization of urushiol from PVP/urushiol membranes. Furthermore, animal test results indicate that when rats are in contact with PVP/urushiol anhydrous ethanol for 48 h, their skins are free from dark brown skin allergy. The presence of PVP eliminates the sensitization of urushiol, and the nanofibrous membranes demonstrate low toxicity. Hence, urushiol is the only natural material that enables PVP to withstand 98% sulfuric acid as well as acquire hydrolyzability, thereby qualify PVP as a medical material.     

Low molecular weight organogelators derived from threefold symmetric tricarbamates

A group of new low molecular weight organogelators based on threefold symmetric tricarbamate were synthesized and characterized. The tricarbamates with long alkyl chains were able to gelate a wide range of polar and nonpolar organic solvents such as acetonitrile and cyclohexane, generally at concentrations lower than 20 g/L. The best organogel formation was obtained using a threefold symmetric tricarbamate in n-dodecane, in which a sufficiently transparent gel was formed at the critical gelation concentration 1 g/L. Intermolecular hydrogen bonding by the tricarbamate in a nonpolar solvent benzene-d₆ was indicated by ¹H NMR spectra. Its maximum UV absorption was 11 nm higher in chloroform than in n-dodecane, and this red shift indicated increased conjugation between the benzene core and the carbamate substituents, which confirmed a change in its conformation from nonpolar to polar solvent. The self-assembling behavior of the tricarbamate in dilute solutions was investigated by TEM. Fiber-like networks were observed in a large range of solution concentrations.     

Counting Simsun Permutations by Descents

We count in the present work simsun permutations of length n by their number of descents. Properties studied include the recurrence relation and real-rootedness of the generating function of the number of n-simsun permutations with k descents. By means of generating function arguments, we show that the descent number is equidistributed over n-simsun permutations and n-André permutations. We also compute the mean and variance of the random variable X _n taking values the descent number of random n-simsun permutations, and deduce that the distribution of descents over random simsun permutations of length n satisfies a central and a local limit theorem as n ?? +???.     

Graphs whose critical groups have larger rank

The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n − 3 and all graphs with r(G) = β(G) = n − 3 are characterized.     

Atoms of multistationarity in chemical reaction networks

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this question is ‘yes’ in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace. We also prove an analogous result when a smaller network is obtained from a larger network by ‘removing species.’ Our results provide the mathematical foundation for a technique used by Siegal- Gaskins et al. of establishing bistability by way of ‘network ancestry.’ Additionally, our work provides sufficient conditions for establishing multistationarity by way of atoms and moreover reduces the problem of classifying multistationary CFSTRs to that of cataloging atoms of multistationarity. As an application, we enumerate and classify all 386 bimolecular and reversible two-reaction networks. Of these, exactly 35 admit multiple positive steady states. Moreover, each admits a unique minimal multistationary subnetwork, and these subnetworks form a poset (with respect to the relation of ‘removing species’) which has 11 minimal elements (the atoms of multistationarity).