Dynamical Casimir Effect for Scalar Fields II (Energy Calculation)

The energy of the evolved vacuum state is calculated. From a frequency cut-off regularisation the divergent terms are separated and, in the 1 + 1 dimensional case they are removed with a mass renormalisation of the moving boundary. A renormalisation of the external force is also needed in 3 + 1 dimensions. PACS Subject Classifications: 42.50.Lc, 03.70.+k, 11.10.Ef.     

Synthesis of 2-amino-5-substituted-1,3,4-oxadiazoles using 1,3-dibromo-5,5-dimethylhydantoin as oxidant

A scalable synthesis of 5-substituted-2-amino-1,3,4-oxadiazoles via oxidation of a thiosemicarbazide precursor is described. The thiosemicarbazide intermediates are easily accessed from the corresponding acid chlorides. Oxidative cyclization using 1,3-dibromo-5,5-dimethylhydantoin as the primary oxidant, in the presence of potassium iodide, gives a variety of oxadiazoles in good yields. This methodology utilizes a commercially inexpensive and easily handled oxidant.     

The nondegenerate center problem and the inverse integrating factor

In this paper we study some aspects of the nondegenerate center problem for analytic and, in particular, for polynomial vector fields. The relation between the existence of an inverse integrating factor and the center problem is studied. The relationship between the conditions for a center using the Poincaré formal series and the inverse integrating factor formal series for systems with a linear center perturbed by homogeneous polynomials is proved.     

Tranversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem

The restricted three-body problem is considered for values of the Jacobi constant C near the value C₂ associated to the Euler critical point L₂. A Lyapunov family of periodic orbits near L₂, the so-called family (c), is born for C = C₂ and exists for values of C less than C₂. These periodic orbits are hyperbolic. The corresponding invariant manifolds meet transversally along homoclinic orbits. In this paper the variation of the transversality is analyzed as a function of the Jacobi constant C and of the mass parameter μ. Asymptotical expressions of the invariant manifolds for C ? C₂ and μ ? 0 are found. Several numerical experiments provide accurate information for the manifolds and a good agreement is found with the asymptotical expressions. Symbolic dynamic techniques are used to show the existence of a large class of motions. In particular the existence of orbits passing in a random way (in a given sense) from the region near one primary to the region near the other is proved.     

On the extendable regular integrals of the n-body problem

It is shown that the n-body problem in a d-dimensional space has no C¹-extendable regular integrals if n ? d + 1.     

Semi-Classical Calculation of the Particle Production in QED via the Schwinger Dynamical Principle

The Schwinger quantum dynamical principle is used to calculate the free vacuum persistence amplitude in the presence of a prescribed electromagnetic background, and the probability that free pairs are created from the vacuum state. An explicit expression of these amplitudes is obtained in the semi-classical approach, showing that, in this approach, the particle production is a stochastic Poisson process. PACS subject classifications. 02.30.Xx, 11.15.Bt, 12.20.Ds, 12.20.-m.     

Orientation-preserving self-homeomorphisms of the surface of genus two have points of period at most two

We show that for any orientation-preserving self-homeomorphism of the double torus there exists a point of such that . This answers a question raised by Jakob Nielsen in 1942.

     

Characterization of acylated flavonoid-O-glycosides and methoxylated flavonoids from Tagetes maxima by liquid chromatography coupled to electrospray ionization tandem mass spectrometry

Liquid chromatography coupled to negative electrospray ionization (ESI) tandem mass spectrometry (MS/MS) employing a triple quadrupole mass spectrometer was used in the structural determination of acylated flavonoid-O-glycosides and methoxylated flavonoids occurring in Tagetes maxima. The compounds were identified by experiments in full scan mode (MS), and tandem mass experiments (MS/MS) of precursor ion scan, product ion scan, and neutral loss scan modes. In order to characterize the aglycones of the flavonoid glycosides, in-source fragmentation of the deprotonated molecule [M-H]- followed by product ion scan of the resulting aglycone [A-H]- were performed. This combined approach allowed the identification of 51 phenolic compounds, including flavonoid-O-glycosides acylated with galloyl, protocatechuoyl, coumaroyl or caffeoyl groups, methoxylated flavonoids, and hydroxycinnamic acid and phenolic acid derivatives, none of them previously reported in Tagetes maxima.     

The first NH aldimine organometallic compound. Isolation and crystal structure

The first NH aldimine organometallic derivative is unexpectedly formed by the cleavage of the nitrogen-carbon bond of the amino acid fragment of the Schiff base 2,4,6-Me3C6H2CH=NCH(CH2Ph)COOEt when the imine is treated with palladium acetate.     

Magneto-structural characterization of metallocene-bridged nitronyl nitroxide diradicals by X-Ray, magnetic measurements, solid-state NMR spectroscopy, and ab initio calculations

Crystallization of ferrocene and ruthenocene substituted in the 1- and 1'-positions by two nitronyl nitroxide radicals gave the new crystal phases beta-1 (besides the known phase alpha-1), alpha-2, and beta-2 whose structures were determined by X-ray analysis. In beta-1 the radical moieties adopt transoid positions, whereas two different cisoid conformations are adopted by alpha-2 and beta-2. These conformations result from inter- and intramolecular hydrogen bonds, respectively. All compounds experience antiferromagnetic interactions, and J/k(B) values up to -7 K have been found by fitting the experimental magnetic susceptibilities to a modified Bleaney-Bowers equation. The solid diradicals alpha-1, beta-1, alpha-2, and beta-2 as well as the ferrocene 3, which was substituted by a unique nitronyl nitroxide, were investigated by (13)C and (1)H NMR spectroscopy with magic angle spinning. The carbon signals cover a range of 2000 ppm, and are well resolved such that the structure could be confirmed. Conversion of the signal shifts into spin densities disclosed the mechanisms by which spin delocalization from the nitronyl nitroxide substituents to the metallocene core occurs. The spin density distribution in alpha-1, beta-1, and 3 was also predicted by DFT calculations. There is good agreement between the experimental and theoretical trends of the spin delocalization. The magnetic interactions were discussed in the light of intramolecular spin transfer and its dependence on geometric constraints, demonstrating that the 1,1'-metallocenylene bridge is not a robust magnetic coupler.