On a minimal set of generators for the invariants of 3 × 3 matrices

Let K be a field of characteristic p > 0, let L be a restricted Lie algebra and let R be an associative K-algebra. It is shown that the various constructions in the literature of crossed product of R with u(L) are equivalent. We calculate explicit formulae relating the parameters involved and obtain a formula which hints at a noncommutative version of the Bell polynomials.     

iVI-TD-DFT: An iterative vector interaction method for exterior/interior roots of TD-DFT

The recently proposed iterative vector interaction (iVI) method for large Hermitian eigenvalue problems (Huang et al., J. Comput. Chem. 2017, 38, 2481) is extended to generalized eigenvalue problems, HC = SCE , with the metric S being either positive definite or not. Although, it works with a fixed-dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The algorithms are further specialized to nonrelativistic and relativistic time-dependent density functional theories (TD-DFT) by taking the orbital Hessian as the metric (i.e., the inverse TD-DFT eigenvalue problem) and incorporating explicitly the paired structure into the trial vectors. The efficacy of iVI-TD-DFT is demonstrated by various examples. © 2018 Wiley Periodicals, Inc.     

外开槽同轴波导传播特性

 根据满足边界条件的一系列电磁场方程,采用场匹配法,详细推导了外开槽同轴波导的特征方程。在外开槽同轴波导光滑内同轴半径等于零的情形下,即变成外开槽圆波导,得到其特征方程。数值模拟了外开槽同轴波导及外开槽圆波导中TE₀₁模式的传播特性,得到了不同尺寸外开槽同轴波导开槽间隙半张角和槽深与特征根的变化关系。结果表明:开槽越深,间隙半张角越小,特征根值越小。     

Evaluation of green and efficient deep eutectic solvents as media for extracting alkaloids from lotus leaf

Deep eutectic solvents (DESs) were applied as eco-friendly solvents in this study for the extraction of alkaloids from lotus leaf, including O-nornuciferine, N-nornuciferine, nuciferine and roemerine. A series of hydrophilic and hydrophobic DESs with different hydrogen bond donors and a acceptors were synthesized and screened for a suitable DESs for extraction of alkaloids from lotus leaf. The study results showed that the hydrophilic DES with choline chloride and propanediol had the highest extraction yield. The main factors affecting the extraction efficiency—choline chloride–propanediol ratio, water content in deep eutectic solvents, solid–liquid ratio and extraction time—were investigated via a single-factor experiment. The optimized extraction conditions were 30% of water in choline chloride–propanediol (1:4) for heated extraction for 30 min and solid–liquid ratio 1:100 g/ml. Under optimum conditions, the extraction yields of O-nornuciferine, N-nornuciferine, nuciferine and roemerine were 0.069, 0.152, 0.334 and 0.041 g/100 g respectively, which were higher than those of methanol in acidified aqueous solution. This study suggests considerable potential for DESs as promising materials for the green and efficient extraction solvents for bioactive alkaloids from natural sources.     

On the imaginary parts of chromatic roots

While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order $n$ (ie, with $n$ vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed $\text{◂+▸}p\in \left(0,1\right)$, almost every random graph $G$ in the Erdös-Rényi model has a nonreal root.     

Practical halving; the Nelumbo nucifera evidence on early eudicot evolution

We present a stepwise optimal genome halving algorithm designed for large eukaryote genomes with largely single-copy genes, taking advantage of a signature pattern of paralog distribution in ancient polyploids. This is applied to the genome of Nelumbo nucifera, the sacred lotus, which is the descendant of a duplicated basal eudicot genome. In concert with the reconstructed ancestor of the grape, we investigate early events in eudicot evolution and show that the chromosome number of the common ancestor of lotus and grape was likely between 5 and 7. We show that the duplication of the ancestor of lotus and the triplication of the ancestor of grape were not closely preceded by any additional such event before the divergence of their two lineages.     

Acute and sub-acute toxicological evaluation of the alcoholic leaf and root extracts of Clerodendrum infortunatum L.

Leaf and root extracts of Clerodendrum infortunatum L. have been reported to show anthelmintic efficacy on a cestode parasite Raillietina tetragona. Its leaf showed no toxicity at 1000 mg/kg body weight but root toxicity study was not known. Therefore, our study is to test both leaf and root extracts at 2000 and 3000 mg/kg body weight concentration given orally for 15 days in four groups of Swiss albino mice, keeping another set as control (without plant extract). Weight and behaviour of mice were recorded daily. Feeding, movement pattern were normal in all treatments as that of control. Though body weight increase, there was no change in the relative organ weight. Biochemical and haematological studies revealed no significant change from control and no alteration in histopathological study of liver and kidney from that of control. The plant extracts thus shown to be safe for consumption.     

Isolation and characterization of four novel β-Sitosteryl esters from Salvadora persica Linn.

Salvadora persica is virtuous to have a variety of phytoconstituents responsible for many biological activities some of them identified particularly while some are still to be acknowledged. A number of steroidal, glycosidic, terpenoids, saponins and functional esters are reported till date. The present study deals with extraction, isolation, and characterisation of four novel steroidal esters by systematic cold extraction of S. persica. The extracted phytoconstituents were characterised by sophisticated spectral UV, IR, NMR and MS, techniques. The reported four new β-Sitosteryl esters SP-2, 3, 5 and 6 were extracted and reported for the first time.     

Determination of lignans,phenolic acids and antioxidant capacity in transformed hairy root culture of Linum usitatissimum

Hairy root culture is a promising alternative method for the production of secondary metabolites. In this study, transformed root of Linum usitatissimum was established using Agrobacterium rhizogenes A4 strain from root cultures for lignans, phenolic acids and antioxidant capacity determination. Total lignin content (secoisolariciresinol diglucoside, secoisolariciresinol and matairesinol) was 55.5% higher in transformed root cultures than in the non-transformed root culture. Secoisolariciresinol was detected in higher concentration (2.107 μmol/g DM) in the transformed root culture than non-transformed culture (1.099 μmol/g DM). Secoisolariciresinol diglucoside and matairesinol were exclusively detected in the transformed root culture, but were not found in the non-transformed root culture. The overall production of phenolic acids in transformed roots was approximately 3.5 times higher than that of the corresponding non-transformed culture. Free radical scavenging DPPH˙ and ABTS˙⁺ assays showed 2.9-fold and 1.76-fold higher anti-oxidant activity in transformed root culture as compared to non-transformed.