偏缠绕模的Frobenius性质

主要给出了偏缠绕模的Frobenius性质，推广了缠绕模相应的性质。     

Synthesis and crystal structures of novel glycoluril carboxylic acids conglomerates

The two novel conglomerates were obtained by crystallization of racemic (2'S,3aS,6aR)/(2'R,3aR,6aS) (glycoluril-1-yl)-3-methylbutanoic acid and (2'R,3aR,6aR)/(2'S,3aS,6aS) (4,6-dimethylglycoluril-1-yl)pentanoic acid synthesized by highly diastereoselective condensation of 4,5-dihydroxy- imidazolidin-2-ones with racemic ureido acids. The differences in the molecular geometry of synthesized racemates were studied by X-ray diffraction that showed them to crystallize as conglomerates in non-centrosymmetric space groups Pna2₁ and P2₁2₁2₁, respectively     

Structure and bonding of lanthanide dinitrogen complexes,Ln(N2)1-8

Lanthanide dinitrogen complexes, Ln(N₂) _x (x = 1-8), were investigated by Density Functional Theory computations using the B3LYP exchange-correlation functional in conjunction with quasirelativistic pseudopotentials for Ln. After a recent study on the lanthanum complexes (A. Kovács, Structural Chemistry 2018 , 29, 1825), the present study aimed to probe the changes upon variously filled 4f subshells of Ln on the structures, stabilities, and bonding properties in related complexes of Nd, Ho, and Lu. The bonding properties were assessed on the basis of natural atomic charges, Ln valence orbital populations, and analysis of bonding molecular orbitals.     

Using principal eigenvectors of adjacency matrices with added diagonal weights to compose centrality measures and identify bowtie structures for a digraph

Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Nanocomposite hydrogel consisting of Na‐montmorillonite with enhanced mechanical properties

A new kind of nanocomposite (NC) hydrogel with Na‐montmorillonite (MMT) is presented in this article. The NC hydrogels were synthesized by free radical copolymerization of acrylamide and (3‐acrylamidopropyl) trimethylammonium chloride (ATC) in the presence of MMT and N,N′‐methylene‐bis‐acrylamide used as chemical cross‐linker. Due to the cation‐exchange reaction between MMT and ATC (cationic monomer) during the synthesis of NC hydrogels, MMT platelets were considered chemical “plane” cross‐linkers, different from “point” cross‐linkers. With increasing amount of MMT, the crosslinking degree enhanced, causing a decrease of the swelling degree at equilibrium. Investigations of mechanical properties indicated that NC hydrogels exhibited enhanced strength and toughness, which resulted from chemical interaction between exfoliated MMT platelets and polymer chains in hydrogels. Dynamic shear measurements showed that both storage modulus and loss modulus increased with increasing MMT content. The idea described here provided a new route to prepare hydrogels with high mechanical properties by using alternative natural Na‐MMT. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1020–1026     

One-pot Synthesis,Crystal Structures and Antimicrobial Activities of Two New 1,4-Disubstituted 1,2,3-Triazole-4-Carboxylates

Two new 1,4-disubstituted 1,2,3-triazoles-4-carboxylates were synthesized via click reaction. Compound 1a was synthesized by the interaction of 6-nitro-tetrazolo[1.5-a]-pyridine with ethyl propynoate at room temperature in the presence of Cu(OAc)2 as a catalyst and THF as solvent. Compound 1b was also synthesized by the same manner except that tert-butyl propionate, instead of ethyl propynoate, was used. The compounds were characterized by IR, 1H-NMR, 13C-NMR and single-crystal X-ray diffraction analysis. Compound 1a(C10H9N5O4) crystallizes in the triclinic system, space group P1 with a = 5.0894(9), b = 8.9834(13), c = 13.089(2) ?, α= 83.041(7), β= 80.256(7), γ=87.296(8)°, V = 585.24(16)?3, Z = 2, Mr = 263.22, crystal size(mm) = 0.37 × 0.20 ×0.18,(I 2σ(I)) = 8557, 2493, 1229, Rint = 0.057. Compound 1b(C12H13N5O4) crystallizes in the monoclinic system, space group P21/c with a = 6.8854(5), b = 21.783(2), c = 9.3986(8) ?,β = 93.239(4)°, V = 1407.4(2)?3, Z = 4, Mr = 291.27, crystal size(mm) = 0.38 × 0.22 × 0.20,(I 2σ(I)) = 11842, 3172, 1866, Rint = 0.047. Antimicrobial assay results showed that the title compounds display excellent activities to different bacterial and fungal strains.     

Electronic structure and absolute band edge position of tetragonal AgInS2 photocatalyst: A hybrid density functional study

Energy bands, effective mass of carriers, absolute band edge positions and optical properties of tetragonal AgInS₂ were calculated using a first-principles approach with the exchange correlation described by B3LYP hybrid functional. The results indicate that tetragonal AgInS₂ has a direct band gap of 1.93 eV, which reproduce well experimental value. Calculated effective masses of electrons and holes are both small which are beneficial to separation and migration of electron and hole pairs. This implies that AgInS₂ has good photocatalytic performance. The calculated optical characteristics indicate that AgInS₂ has a slight anisotropy for both the real and imaginary parts of the dielectric function and exhibits large optical absorption in the visible light region. Furthermore, the calculated band edge positions in (100), (010) and (001) surfaces indicate that tetragonal AgInS₂ is beneficial to the reduction and oxidation of water to hydrogen and oxygen under visible light irradiation.     

Wave-based vibration control of large cable net structures

Large cable net structures have been widely applied in aerospace engineering due to the feature of light-weight, high packaging efficiency, and high thermal stability. Structural vibrations induced by a variety of disturbances are inevitable in the space environment, resulting in the requirement of effective vibration control strategies for large cable net structures. Since the large cable net structures have many closely spaced vibrational modes in the range of low frequencies, traditional modal based control may cause modal truncation and spillover problems. In this paper, a wave-based boundary control strategy is adopted and its effectiveness to control the vibration of cable net structures is investigated, by transfer function analysis and numerical methods. It is found that the structural vibration can be absolutely resisted by applying the wave-based boundary controllers onto all the exterior nodes, when disturbances come from the external boundaries of the cable net. Our results in this paper can provide a theoretical basis for the vibration control of large cable net structures.