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.     

Statistical Optimization of Flavonoid and Antioxidant Recovery from Macerated Chinese and Malaysian Lotus Root (Nelumbo nucifera) Using Response Surface Methodology

In this study, the combination of parameters required for optimal extraction of anti-oxidative components from the Chinese lotus (CLR) and Malaysian lotus (MLR) roots were carefully investigated. Box–Behnken design was employed to optimize the pH (X₁: 2–3), extraction time (X₂: 0.5–1.5 h) and solvent-to-sample ratio (X₃: 20–40 mL/g) to obtain a high flavonoid yield with high % DPPH_sc free radical scavenging and Ferric-reducing power assay (FRAP). The analysis of variance clearly showed the significant contribution of quadratic model for all responses. The optimal conditions for both Chinese lotus (CLR) and Malaysian lotus (MLR) roots were obtained as: CLR: X₁ = 2.5; X₂ = 0.5 h; X₃ = 40 mL/g; MLR: X₁ = 2.4; X₂ = 0.5 h; X₃ = 40 mL/g. These optimum conditions gave (a) Total flavonoid content (TFC) of 0.599 mg PCE/g sample and 0.549 mg PCE/g sample, respectively; (b) % DPPH_sc of 48.36% and 29.11%, respectively; (c) FRAP value of 2.07 mM FeSO₄ and 1.89 mM FeSO₄, respectively. A close agreement between predicted and experimental values was found. The result obtained succinctly revealed that the Chinese lotus exhibited higher antioxidant and total flavonoid content when compared with the Malaysia lotus root at optimum extraction condition.     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Multiconstituent identification in root,branch, and leaf extracts of Juglans mandshurica using ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry

As a traditional medicinal plant, Juglans mandshurica has been used for the treatment of cancer. Different organs of this plant showed anti‐tumor activity in clinic and laboratory. Comparative identification of constituents in different plant organs is essential for investigation of the relationship between chemical constituents and pharmacological activities. For this aim, the roots, branches, and leaves of J. mandshurica were extracted with 50% v/v methanol and then subjected to ultra‐high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry analysis conducted under low and high energy. As a result, we have to date identified 111 compounds consisting of 56 tannins, 29 flavonoids, 13 organic acids, 8 naphthalene derivatives, and 5 anthracenes. Five compounds, namely, diquercetin trihydroxy‐truxinoyl‐glucoside, two quercetin kaempferol dihydroxy‐truxinoyl‐glucosides, syringoyl‐tri‐galloyl‐O‐glucose, and dihydroxy‐naphthalene syringoyl‐glucoside, were tentatively identified as new compounds. Of the compounds identified, 76 were found in the root extract, 67 in the branch extract, and 37 in the leaf extract. Only six compounds including four organic acids and two tannins were found in all three extracts. We developed a rapid and sensitive ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry approach to identify multiple constituents of complex extracts without separation and ion selection. The results presented provide useful information on further research of the bioactive compounds of J. mandshurica .     

Finding Adam in random growing trees

We investigate algorithms to find the first vertex in large trees generated by either the uniform attachment or preferential attachment model. We require the algorithm to output a set of K vertices, such that, with probability at least , the first vertex is in this set. We show that for any ε, there exist such algorithms with K independent of the size of the input tree. Moreover, we provide almost tight bounds for the best value of K as a function of ε. In the uniform attachment case we show that the optimal K is subpolynomial in , and that it has to be at least superpolylogarithmic. On the other hand, the preferential attachment case is exponentially harder, as we prove that the best K is polynomial in . We conclude the paper with several open problems. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 158–172, 2017     

An analysis on the efficiency of Euler's method for computing the matrix pth root

It is shown that the matrix sequence generated by Euler's method starting from the identity matrix converges to the principal pth root of a square matrix, if all the eigenvalues of the matrix are in a region including the one for Newton's method given by Guo in 2010. The convergence is cubic if the matrix is invertible. A modification version of Euler's method using the Schur decomposition is developed. Numerical experiments show that the modified algorithm has the overall good numerical behavior.     

Development of models for prediction of the antioxidant activity of derivatives of natural compounds

Antioxidants are important for maintaining the appropriate balance between oxidizing and reducing species in the body and thus preventing oxidative stress. Many natural compounds are being screened for their possible antioxidant activity. It was found that a mushroom pigment Norbadione A, which is a pulvinic acid derivative, shows an antioxidant activity; the same was found for other pulvinic acid derivatives and structurally related coumarines. Based on the results of in vitro studies performed on these compounds as a part of this study quantitative structure–activity relationship (QSAR) predictive models were constructed using multiple linear regression, counter-propagation artificial neural networks and support vector regression (SVR). The models have been developed in accordance with current QSAR guidelines, including the assessment of the models applicability domains. A new approach for the graphical evaluation of the applicability domain for SVR models is suggested. The developed models show sufficient predictive abilities for the screening of virtual libraries for new potential antioxidants.     

Limit distribution of the coefficients of polynomials with only unit roots

We consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if and only if the fourth central and normalized (by the standard deviation) moment tends to 3, in contrast to the common scenario for polynomials with only real roots for which a central limit theorem holds if and only if the variance is unbounded. We also derive a representation theorem for all possible limit laws and apply our results to many concrete examples in the literature, ranging from combinatorial structures to numerical analysis, and from probability to analysis of algorithms. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,707–738, 2015