How to distinguish between cinnamoylshikimate esters and chlorogenic acid lactones by liquid chromatography-tandem mass spectrometry

In this study, liquid chromatography–tandem mass spectrometry (LC–MSⁿ; n = 2–3) has been used to characterize and distinguish chlorogenic acid lactones from cinnamoylshikimate esters. This is the first time when an LC–MSⁿ method has been developed to distinguish between these two isomeric classes of compounds formed in particular in food processing from chlorogenic acids at elevated temperature through loss of water. The structures of regioisomeric chlorogenic acid lactones and shikimate esters have been assigned on the basis of LC–MSⁿ patterns of fragmentation, relative hydrophobicity, and fragmentation analogy with the synthetic standards of dimethoxycinnamic, ferulic, and caffeic acid containing monoacyl chlorogenic acid lactones and shikimate esters. Copyright © 2011 John Wiley & Sons, Ltd.     

Design, Synthesis and Photostability of Novel 1,8-naphthalimide PAMAM Light-harvesting Dendrons

This paper reports on the divergent synthesis, photophysical properties and photodegradation of novel PAMAM dendrons, core and peripherally functionalized with 1,8-naphthalimide fluorophores. The novel compounds were configured as light-harvesting antennae where the system surface is labeled with blue emitting 4-allyloxy-1,8-naphthalimide ??donor?? fluorophores capable of absorbing light and efficiently transferring the energy to a single yellow-green emitting 4-alkylamino-1,8-naphthalimide ??acceptor?? dye. The focal 1,8-naphthalimide fluorophores in the antennae were modified with a HALS fragment (2,2,6,6-tetramethylpiperidine or 1,2,2,6,6-pentamethylpiperidine) with a view to improve their photostability. Novel light-harvesting systems showed highly efficient energy transfer, depending on the volume of the core substituent. Due to the HALS fragments the chromophoric system of the novel antennae showed higher photostability, while the photostability of the PAMAM scaffold was found to be lower.     

Crystal and molecular structure of 9-methyl-9-phenyl-9,10-dihydro-9-sila-3-azaanthrone

The crystal and molecular structure of 9-methyl-9-phenyl-9,10-dihydro-9-sila-3-azaanthrone has been determined from three-dimensional X-ray diffraction data. The title compound crystals are monoclinic, space group P2₁/b, a = 12.818(2), b = 16.508(2), c = 7.694(1) Å,γ = 105°, 34′(2), Z = 4 and D_cal = 1.278 g cm^?3. The structure was determined by direct methods and refined by full-matrix least-squares calculations in the block-diagonal anisotropic approximation for non-hydrogen atoms to R = 0.043 for 2190 independent reflections, registered at room temperature. This is the first crystal structure determination of a Si-dihydroanthracene derivative with two heterocycles and a planar carbon atom in the C10-position. The tricyclic fragment takes up a planar configuration, the silicon atom having a tetrahedral surrounding, with an endocyclic angle of 103.7(1)° and average bond length SiC, 1.862(1) Å. The CO, 1.220(2) Å, bond length in the carbonylic group exactly corresponds with the double bond length. Average distance NC is 1.335(3) Å, angle CNC, 116.5(2)°.     

Continuity of Dirac spectra

It is well known that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article, we extend this result to a global version. We view the spectrum of a Dirac operator as a function $\mathbb Z \,\rightarrow \mathbb R \,$ and endow the space of all spectra with an $\mathrm{arsinh }$ -uniform metric. We prove that the spectrum of the Dirac operator depends continuously on the Riemannian metric. As a corollary, we obtain the existence of a non-decreasing family of functions on the space of all Riemannian metrics, which represents the entire Dirac spectrum at any metric. We also show that, due to spectral flow, these functions do not descend to the space of Riemannian metrics modulo spin diffeomorphisms in general.     

Differential invariants of a class of Lagrangian systems with two degrees of freedom

We consider systems of Euler–Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie?s infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.     

On “new travelling wave solutions” of the KdV and the KdV–Burgers equations

The Korteweg-de Vries and the Korteweg-de Vries–Burgers equations are considered. Using the travelling wave the general solutions of these equations are presented. “New travelling wave solutions” of the KdV and the KdV–Burgers equations by Wazzan [Wazzan L. Commun Nonlinear Sci Numer Simulat 2009;14:443–50] are analyzed. We demonstrate that all his solutions are not new and are transformed to known solutions.     

A description of Baer-Suzuki type of the solvable radical of a finite group

We obtain the following characterization of the solvable radical R(G) of any finite group G: R(G) coincides with the collection of all g∈G such that for any 3 elements a₁,a₂,a₃∈G the subgroup generated by the elements , i=1,2,3, is solvable. In particular, this means that a finite group G is solvable if and only if in each conjugacy class of G every 4 elements generate a solvable subgroup. The latter result also follows from a theorem of P. Flavell on {2,3}^′-elements in the solvable radical of a finite group (which does not use the classification of finite simple groups).     

Multi-particle dynamical systems and polynomials

Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi-particle dynamical system by finding polynomial solutions of partial differential equations is introduced. The method enables one to integrate a wide class of polynomial multi-particle dynamical systems. The general solutions of certain dynamical systems related to linear second-order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived.     

Global regular solutions for the 3D Kawahara equation posed on unbounded domains

An initial boundary value problem for the 3D Kawahara equation posed on a channel-type domain was considered. The existence and uniqueness results for global regular solutions as well as exponential decay of small solutions in the H²-norm were established.