Permutation groups generated by cycles of fixed length

Combinatorial conditions on a set of cycles of fixed degree inS _n are studied, so that they generateA _n orS _n . It is shown thatA _n orS _n is so generated if and only if a graph associated with the set of cycles is connected, provided two of the cycles satisfy certain, not too restrictive, criteria. As a corollary, the minimum number of cycles of degreem ≧ 2 that generateA _n or S_n is determined.     

Passively mode-locked Yb:KLu(WO4)2 thin-disk oscillator operated in the positive and negative dispersion regime

We demonstrate a passively mode-locked femtosecond Yb:KLu(WO(4))(2) thin-disk laser oscillator. Chirped-pulse operation in the positive dispersion regime as well as solitary operation have been realized, and the laser performance of both configurations are compared. In the solitary mode-locking regime the output power exceeds 25 W in a diffraction-limited beam, and pulse durations as short as 440 fs at a 34.7 MHz repetition rate have been generated. For the first time we present a chirped-pulse operation of a thin-disk oscillator that yields a maximum average output power of 9.5 W with a Fourier limit of 450 fs.     

Correlation measure to detect time series distances, whence economy globalization

An instantaneous time series distance is defined through the equal time correlation coefficient. The idea is applied to the Gross Domestic Product (GDP) yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation. Some data discussion is first presented to decide what (EKS, GK, or derived) GDP series should be studied. Distances are then calculated from the correlation coefficient values between pairs of series. The role of time averaging of the distances over finite size windows is discussed. Three network structures are next constructed based on the hierarchy of distances. It is shown that the mean distance between the most developed countries on several networks actually decreases in time, —which we consider as a proof of globalization. An empirical law is found for the evolution after 1990, similar to that found in flux creep. The optimal observation time window size is found ?15 years.     

Has the world economy reached its globalization limit?

The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the “richest” countries are examined. Four types of “distances” are calculated. Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best characterised by an entropy measure, based on entropy Manhattan distance. It is observed that a globalization maximum was reached during the interval 1970-2000. More recently a deglobalization process has been observed.     

A-stable Runge–Kutta methods for semilinear evolution equations

We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. In this setting, we prove the existence of solutions which are temporally smooth in the norm of the lowest rung of the scale for an open set of initial data on the highest rung of the scale. Under the same assumptions, we prove that a class of implicit, A-stable Runge–Kutta semidiscretizations in time of such equations are smooth as maps from open subsets of the highest rung into the lowest rung of the scale. Under the additional assumption that the linear part of the evolution equation is normal or sectorial, we prove full order convergence of the semidiscretization in time for initial data on open sets. Our results apply, in particular, to the semilinear wave equation and to the nonlinear Schrödinger equation.     

Ground states in non-relativistic quantum electrodynamics

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state – one that minimizes the energy and satisfies the Schr?dinger equation. We prove quite generally that this state exists for all values of the fine-structure constant and the ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions. Oblatum 21-IX-2000 & 8-IV-2001?Published online: 18 June 2001     

Covering the alternating groups by products of cycle classes

Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99].     

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of α^3/2, α being the fine structure constant. A suitably chosen ground state vector depends analytically on α^3/2 and it is twice continuously differentiable with respect to the nuclear coordinates. Submitted: November 24, 2008. Accepted: March 4, 2009.     

Ultra-fast chromatographic micro-assay for quantification of diphenidol in plasma: application in an oral multi-dose switchability trial

Pharmacokinetics of diphenidol (DPN) is limited due to the lack of analytical methodology. Here, a micro-assay for DPN quantification was developed, by coupling ultra-performance liquid chromatography with tandem mass spectrometry. The procedure involved plasma precipitation and injection of supernatant into UPLC with an Acquitytrade mark C18 column. Detection was in positive electrospray, following transitions of m/z 310.3 --> 292.3 and m/z 275.3 --> 230.2 for DPN and chlorphenamine (internal standard), respectively. The method was linear with a range of 4-400 ng/mL, and a 2 min run time. This method was applied in a switchability trial, where both formulations of DPN were bioequivalent.     

Iridium derivatives of fluorinated aromatics by C-H activation: isolation of classical and non-classical hydrides

A reaction of trans-[Ir(H)(5)(PiPr(3))(2)] (1) with 2,3,5,6-tetrafluoropyridine, pentafluorobenzene or 1,3-difluorobenzene in the presence of neohexene affords the square-pyramidal C-H activation products cis-trans-[Ir(4-C(5)NF(4))(H)(2)(PiPr(3))(2)] (2), cis-trans-[Ir(C(6)F(5))(H)(2)(PiPr(3))(2)] (4) and cis-trans-[Ir(2-C(6)H(3)F(2))(H)(2)(PiPr(3))(2)] (6). Irradiation of complex 1 with 2,3,5,6-tetrafluoropyridine or pentafluorobenzene gave the hydrides cis-trans-[Ir(4-C(5)NF(4))(H)(2)(H(2))(PiPr(3))(2)] (3) or cis-trans-[Ir(C(6)F(5))(H)(2)(H(2))(PiPr(3))(2)] (5). The presence of non-classical bound H(2) moieties has been demonstrated by the measurement of T(1) times at different temperatures. For 3 the H-H distance in the H(2) ligand can be estimated to be 0.82 A. The dihydride compounds 2, 4 and 6 react with CO to yield the complexes cis-trans-[Ir(Ar)(H)(2)(CO)(PiPr(3))(2)] (7: Ar = 4-C(5)NF(4), 8: Ar = C(6)F(5), 9: Ar = 2-C(6)H(3)F(2)). A reaction of 2 or 3 with an excess of ethylene leads to the formation of ethane and the Ir(i) ethylene complex trans-[Ir(4-C(5)NF(4))(eta(2)-C(2)H(4))(PiPr(3))(2)] (10). Treatment of 10 with CO furnishes the Ir(i) complex trans-[Ir(4-C(5)NF(4))(CO)(PiPr(3))(2)] (11).