Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Qualitative and quantitative determination of Atractylodes rhizome using ultra‐performance liquid chromatography coupled with linear ion trap–Orbitrap mass spectrometry with data‐dependent processing

A quick and effective workflow based on ultra‐performance liquid chromatography coupled with electron spray ionization and LTQ‐Orbitrap mass spectrometry (UPLC‐LTQ‐Orbitrap MS) was established for compositional analysis and screening of the characteristic compounds of three species of Atractylodes rhizome for quality evaluation. This technique was employed to determine the seven main components in Atractylodes rhizome samples. Ultimately, 78 constituents were identified; of these, seven characteristic compounds were selected for species discrimination, comprising atractylodin (63), atractylenolide I (43), atractylenolide II (49), atractylenolide III (53), atractylon (69), methyl‐atractylenolide II (54) and (4E,6E,12E)‐tetradecadecatriene‐8,10‐diyne‐1,3‐diacetate (59). The seven main compounds, including six characteristic compounds, were simultaneously determined in 29 batches of Atractylodes rhizome samples. Thus, the method validation showed acceptable results. Quantitative analysis showed significantly different contents of the seven main components among the three species of Atractylodes rhizome, which indicates possible distinctions in the pharmacological effects. This established method can simultaneously provide qualitative and quantitative results for compositional characterization of Atractylodes rhizomes and for quality control.     

Preparation and characterization of new inorganic–organic hybrid catalyst H3PMo12O40/Hyd‐SBA‐15 and its application in the domino multi‐component reaction

We present novel inorganic–organic hybrid catalyst to accomplish domino multi‐component reaction (MCR) for synthesis of 3‐amino‐2′‐oxospiro[benzo[c]pyrano[3,2‐a]phenazine‐1,3′‐indoline]‐2‐carbonitrile/carboxylate derivatives. This methodology offers remarkable development by easy production of H₃PMo₁₂O₄₀/Hyd‐SBA‐15 in regard to solving the problem of using harsh catalysts, also it demonstrates to be impressive and environmentally friendly in term of low reaction times and high yields.     

Normal halogen dependence of 13C NMR chemical shifts of halogenomethanes revisited at the four‐component relativistic level

The ‘Normal Halogen Dependence’ of ¹³C NMR chemical shifts in the series of halogenomethanes is revisited at the four‐component relativistic level. Calculations of ¹³C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four‐component relativistic theory of Dirac‐Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyall's basis sets of triple‐zeta quality or higher are to be used within the framework of the four‐component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non‐relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates

We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.     

Metabolites identification of oil palm roots infected with Ganoderma boninense using GC–MS-based metabolomics

An approach to metabolomics profiling of non-infected and Ganoderma boninense (G. boninsense) infected oil palm roots crude extracts that utilize gas chromatography-mass spectrometry (GC–MS) and multivariate statistics of principal component analysis (PCA) have been tested. This combination has provided a rapid approach in investigating the changes in the metabolite variations of non-infected and infected oil palm roots at 14 and 30 days post-infection. The extracts were prepared by using 80% (v/v) of methanol. In identifying the metabolites responsible for each differentiation, PCA model was generated in loading bi-plot. Dimethyl benzene-1,4-dicarboxylate, methyl 3-(3,5-ditert-butyl-4-hydroxyphenyl)propanoate, ergost-5-en-3-ol, (3β), stigmast-5-en-3-ol, (3β), stigmasterol, methyl hexadecanoate, methyl (9Z,12Z)-octadeca-9,12-dienoate, methyl octadecanoate, 2-(hydroxymethyl)-2-nitropropane-1,3-diol, methyl (Z)-octadec-6-enoate and (E)-icos-5-ene were found more abundant in G. boninense infected roots than in non-infected roots. Steroidal compounds and fatty acid derivatives which has been determined in the non-infected and G. boninense infected roots regulate a variety of responses to the G. boninense. The abundant of these metabolites in G. boninense infected roots are due to the crucial roles in pathogen defence.