Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Controlled synthesis of ZnO nanoparticles from a Zn(II) coordination polymer: Structural characterization,optical properties and photocatalytic activity

A zinc coordination polymer derived from pyridine-2,6-dicarboxylate (PDC), {[Zn₂(PDC)₂]}_n, was successfully prepared via conventional, sonication and microwave-irradiation methods. The composition and characteristics of the obtained coordination polymers (CPs) were investigated by elemental analysis, TGA/DTA, X-ray diffraction and spectroscopic techniques. The so obtained CPs were heat-treated in the air at 600 °C for 2 h to produce ZnO of nanosized particles (NPs). It is of interest to note that the synthesis approach of the precursor greatly affects both the nanoparticle size and the structure of the resulting ZnO NPs. Moreover, the smallest particle size was associated with the sample derived from the ultrasonically prepared precursor. TEM analysis revealed that all samples have sphere-like morphologies. Structural analysis of the prepared ZnO samples was conducted and compared using Rietveld analysis of their PXRD patterns. Optical band gap calculations based on analysis of the UV–vis spectra of ZnO samples using Tauc's power law were achieved. The highest band gap of 3.63 eV was observed for ZnO sample obtained from the ultrasonically prepared precursor. Furthermore, the photocatalytic activity of ZnO NPs for the removal of Eosin Y color was monitored. The highest removal efficiency was recorded for ZnO originated from the ultrasonically synthesized precursor. Enhancement of removal efficiency that reached 98% was attained in only a period of 8 min. Its recycling test showed that it can be reused without structural changes over four cycling experiments.     

Comparative absorption kinetics of seven active ingredients of Eucommia ulmoides extracts by intestinal in situ circulatory perfusion in normal and spontaneous hypertensive rats

Eucommia ulmoides Oliv. (E. ulmoides) is a valuable and nourishing medicinal herb in China that has been used in the treatment of hypertension. Given the fact that most traditional Chinese medicine is mainly used to treat disease, investigating the pharmacokinetics of traditional Chinese medicines in the pathological state is more useful than that in the normal state. However, the differences in the absorption kinetics of active ingredients of E. ulmoides extract between pathological and physiological conditions have not been reported. Therefore, in this study, the rat intestinal in situ circulatory perfusion model was used to investigate the differences in absorption kinetics of seven active ingredients of E. ulmoides extract in normal and spontaneously hypertensive rats, namely, genipinic acid, protocatechuic acid, neochlorogenic acid, chlorogenic acid, cryptochlorogenic acid, (+)-pinoresinol di-O-β-D -glucopyranoside and (+)-pinoresinol 4′-O-β-D -glucopyranoside. Our results indicate that the pathological state of spontaneous hypertension may change the absorption of active components of E. ulmoides extracts, and these findings may provide a reference for improving the rational use of E. ulmoides in the clinic.     

Enhancing the Water Stability of Al‐MIL‐101‐NH2 via Postsynthetic Modification

The resistance of metal–organic frameworks towards water is a very critical issue concerning their practical use. Recently, it was shown for microporous MOFs that the water stability could be increased by introducing hydrophobic pendant groups. Here, we demonstrate a remarkable stabilisation of the mesoporous MOF Al‐MIL‐101‐NH₂ by postsynthetic modification with phenyl isocyanate. In this process 86 % of the amino groups were converted into phenylurea units. As a consequence, the long‐term stability of Al‐MIL‐101‐URPh in liquid water could be extended beyond a week. In water saturated atmospheres Al‐MIL‐101‐URPh decomposed at least 12‐times slower than the unfunctionalised analogue. To study the underlying processes both materials were characterised by Ar, N₂ and H₂O sorption measurements, powder X‐ray diffraction, thermogravimetric and chemical analysis as well as solid‐state NMR and IR spectroscopy. Postsynthetic modification decreased the BET equivalent surface area from 3363 to 1555 m² g^?1 for Al‐MIL‐101‐URPh and reduced the mean diameters of the mesopores by 0.6 nm without degrading the structure significantly and reducing thermal stability. In spite of similar water uptake capacities, the relative humidity‐dependent uptake of Al‐MIL‐101‐URPh is slowed and occurs at higher relative humidity values. In combination with ¹H‐²⁷Al D ‐HMQC NMR spectroscopy experiments this favours a shielding mechanism of the Al clusters by the pendant phenyl groups and rules out pore blocking.     

Dinuclear gold (I)-di-N-heterocyclic carbene complexes: syntheses,structure, density functional theory calculation and photoluminescence study

The synthesis and characterizations for a series of dinuclear gold (I)-di-NHC complexes, 1–8 through the trans-metalation method of their respective silver (I)-di-NHC complexes, i–viii are reported (where NHC = N-heterocyclic carbene). The successful complexation of a series of unusual non-symmetrical and symmetrical di-NHC ligands, 3,3'-(ethane-1,2-diyl)-1-alkylbenzimidazolium-1'-butylbenzimidazolium (with alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, benzyl) with the gold (I) ions are suggested by elemental analysis, Fourier transform-infrared, ¹H- and ¹³C-NMR data. The ¹³C-NMR spectra of 1–8 show a singlet sharp peak in the range of 190.00–192.00 ppm, indicating the presence of a carbene carbon that bonded to the gold (I) ion. From single crystal X-ray diffraction data, the structure of complex 6 with the formula of [di-NHC-Au (I)]₂·2PF₆ is obtained [where NHC = 3,3'-(ethane-1,2-diyl)-1-hexylbenzimidazolium-1'-butylbenzimidazolium]. The photophysical study in solid state of 6 displays an intense photoluminescence with a strong emission maxima, λ_em = 480 nm, upon excitation at 340 nm at room temperature. Interestingly, the emission maximum at 77 K shows a structural character with a strong peak at 410 nm, a medium at 433 nm and a weak at 387 nm, accompanied by a tail band to about 500 nm.     

Synthesis,Crystal Structure,and Magnetic Properties of a New Dinuclear Iron Complex with Schiff Base Ligand

A new dinuclear iron(Ⅲ) complex has been synthesized and structurally characterized by X-ray crystallography: [FeⅢ2(L)(C6H5COO)(SO4)(CH3OH)2]·CH3CN·CH3OH(1, H3 L = N,N'-bis(salicylidene)-1,3-diamino-2-propanol). Complex 1 belongs to orthorhombic space group Pna21 with a = 11.4400(8), b = 22.9705(2), c = 12.5712(9) , V = 3303.5(4) 3, Z = 4, F(000) = 1576, Dc = 1.531 g·cm–3, Mr = 761.36, μ = 1.007 mm–1, S = 1.014, the final R = 0.0505 and wR = 0.1018. The crystal packing is stabilized by intermolecular O–H···O hydrogen bonds, forming an extended one-dimensional chain structure. The temperature dependence of magnetic susceptibility measurement shows that antiferromagnetic interaction is propagated between the metal centers. Fit as dinuclear arrangement gave parameters of J = 19.7 cm-1, g = 1.89 and R2 = 0.9999.     

Novel halogenated cyclopentasilylene-2,4-dienes via DFT

In view of immense importance of silylenes and the fact that their properties undergo significant changes on substitution with halogens, here, we have used B3LYP/6-311++G** level of theory to access the effects of 1–4 halogens (X = F, Cl, Br, and I) on four unprecedented sets of cyclopentasilylene-2,4-dienes; with the following formulas: SiC₄H₃X ( 1 _X ), SiC₄H₂X₂ ( 2 _X ), SiC₄HX₃ ( 3 _X ), and SiC₄X₄ ( 4 _X ). In going down from F to I, the singlet (s)-triplet (t) energy gap (ΔE_s-t, a possible indication of stability), and band gap (ΔE_H-L) decrease while nucleophilicity (N), chemical potential (μ), and proton affinity (PA) increase. The overall order of N, μ, and PA for each X is 2 _X > 1 _X > 3 _X > 4 _X . Precedence of 2 _X over 1 _X is attributed to the symmetric cross conjugation in the former. The highest and lowest N are shown by 2 _I and 4 _F . The trend of divalent angle () for each X is 4 _X > 1 _X > 3 _X > 2 _X . The results show that in going from electron withdrawing groups (EWGs) to electron donating groups (EDGs), the ΔE_s-t and ΔE_H-L decrease while N, μ, and PA increase. Also, rather high N of our scrutinized silylenes may suggest new promising ligands in organometallic chemistry.     

非线性互补问题的一种全局收敛的显式光滑Newton方法

本针对Po函数非线性互补问题，给出了一种显式光滑Newton方法，该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程，并在适当的假设条件下，证明了算法的全局收敛性。     

Lagrangian for the t–J Model Constructed from the Generators of the Supersymmetric Hubbard Algebra

In order to describe the dynamics of the t–J model, two different families of first-order Lagrangians in terms of the generators of the Hubbard algebra are found. Such families correspond to different dynamical second-class constrained systems. The quantization is carried out by using the path-integral formalism. In this context the introduction of proper ghost fields is needed to render the model renormalizable. In each case the standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. In the first case a nonperturbative large-N expansion is considered with the purpose of studying the generalized Hubbard model describing N-fold-degenerate correlated bands. In this case the 1/N correction to the renormalized boson propagator is computed. In the second case the perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details. As an example the thermal softening of the magnon frequency is computed. The antiferromagnetic case is also analyzed, and the results are confronted with previous one obtained by means of the spin-polaron theories.     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.