Octonions and Singular Solutions of Hessian Elliptic Equations

Algebra of Octonions is used to construct singular viscosity solutions of fully nonlinear Hessian elliptic equations. These equations are written in the form of an Isaacs equation.     

Using Competitive Population Evaluation in a differential evolution algorithm for dynamic environments

This paper proposes two adaptations to DynDE, a differential evolution-based algorithm for solving dynamic optimization problems. The first adapted algorithm, Competitive Population Evaluation (CPE), is a multi-population DE algorithm aimed at locating optima faster in the dynamic environment. This adaptation is based on allowing populations to compete for function evaluations based on their performance. The second adapted algorithm, Reinitialization Midpoint Check (RMC), is aimed at improving the technique used by DynDE to maintain populations on different peaks in the search space. A combination of the CPE and RMC adaptations is investigated. The new adaptations are empirically compared to DynDE using various problem sets. The empirical results show that the adaptations constitute an improvement over DynDE and compares favorably to other approaches in the literature. The general applicability of the adaptations is illustrated by incorporating the combination of CPE and RMC into another Differential Evolution-based algorithm, jDE, which is shown to yield improved results.     

NMR-Based Metabolomic Analyses to Identify the Effect of Harvesting Frequencies on the Leaf Metabolite Profile of a Moringa oleifera Cultivar Grown in an Open Hydroponic System

Moringa oleifera Lam. is one of the world’s most useful medicinal plants. Different parts of the M. oleifera tree contain a rich profile of important minerals, proteins, vitamins, and various important bioactive compounds. However, there are differences in the phytochemical composition of the medicinal plant’s raw materials due to seasonal variation, cultivation practices, and post-harvest processing. The main objective of this study was therefore to determine the effect of harvesting frequencies on selected bioactive compounds of a M. oleifera cultivar (PKM1) grown in a hydroponic system under a shade net structure. Three harvesting frequency treatments were applied in the study, with the plants harvested at every 30 days (high frequency), 60 days (intermediate frequency), and 90 days (low frequency) respectively. ¹H-NMR was used for data acquisition, and multivariate data analysis by means of principal component analysis (PCA), partial least square discriminatory analysis (PLS-DA), and orthogonal partial least square discriminatory analysis (OPLS-DA) were applied to determine the changes in the leaf metabolite profile, and also to identify the spectral features contributing to the separation of samples. Targeted metabolite analysis was used to match the NMR peaks of the compounds with the NMR chemical shifts of the contribution plot. The contribution plot showed that the increase in concentration of some compounds in aliphatic, sugar and aromatic regions contributed to the separation of the samples. The results revealed that intermediate and low harvesting frequencies resulted in a change in the leaf metabolite profile. Compounds such as chlorogenic acid, ferulic acid, vanillic acid, wogonin, esculetin, niazirin, and gamma-aminobutyric acid (GABA) showed an increase under intermediate and low harvesting frequencies. These results provide insight into the effect of harvesting frequencies on the metabolite profile and associated medicinal activity of M. oleifera.     

Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation

A new developed approximation is used to obtain the arbitrary l‐wave bound and scattering state solutions of Schrödinger equation for a particle in a hyperbolic‐type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov–Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results. For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method. © 2015 Wiley Periodicals, Inc.     

Projective ideals of skew polynomial rings over HNP rings

Let R be an hereditary Noetherian prime ring (or, HNP-ring, for short), and let S?=?R[x;σ] be a skew polynomial ring over R with σ being an automorphism on R. The aim of the paper is to describe completely the structure of right projective ideals of R[x;σ] where R is an HNP-ring and to obtain that any right projective ideal of S is of the form X𝔟[x;σ], where X is an invertible ideal of S and 𝔟 is a σ-invariant eventually idempotent ideal of R.     

呋虫胺衍生物杀虫活性的理论研究

基于Chem3D Ultra 7.0软件中的MOPAC半经验方法 AM1,计算了13种呋虫胺衍生物的19个量子化学和理化参数(包括ELUMO、EHOMO、△E=ELUMO-EHOMO、QC1、QC2、QN、QN1~QN4、QO、QO、μ、Hf、Ve、E0、Cv、Sm等)。采用最佳变量子集回归方法,建立呋虫胺衍生物对褐飞虱杀虫活性与上述结构参数的定量构效关系模型。结果表明,呋虫胺衍生物对褐飞虱杀虫活性的大小与ELUMO、QN1呈负相关,而与QC2正相关。所建的最优三变量模型具有良好的预报能力(R2=0.928、Rcv2=0.805、Rcv-22=0.797)和较高的稳健性(Radj2、F、VIF、t、AIC和FIT等检验)。设计与预测了4种新颖化合物的杀虫活性,在浓度为500mg/dm3下,它们的杀虫活性预测值均超过115%。所建模型可为化学工作者合成新型高效新烟碱类化合物提供理论参考。     

Ein allgemeiner Satz der Integrirbarkeitslehre

Ohne Zusammenfassung     

在激光大气传输中利用SBS阈值效应实现小面积信标的研究

 在理论上建立起将受激布里渊散射（SBS）与激光大气传输过程相结合的激光补偿传输的数学模型,并进行了数值模拟，提出并证明了利用SBS阈值效应可以将相位共轭光会聚到目标上一个小面积上，从而在目标上主动获得小面积信标光斑。利用SBS实现激光大气补偿传输（传输距离250m）的实验研究,证实了上述理论预期。