A lower bound on the length of a sequence containing all permutations as subsequences

A lower bound on the length of a sequence containing n symbols that has every permutation of those symbols as a subsequence, is obtained. The bound is of the form $\text{n}{}^2\text{? cn}{}^{\mathrm{<mtext>7</mtext><mtext>4+?</mtext>}}$, for ? > 0; the best examples have length n² ? 2n + 4. The method is inductive.     

Topological and metric product\mathbb{Z}^d -actions and their applications-actions and their applications

We show that for a -action Ψ being the Kronecker sum of a symbolic strictly ergodic -actionT and a Chacon -actionS, the rank (covering number) of Ψ is the same as that forT. Using this result we construct, for a given natural numberr≥2 and a real numberb∈(0,1) withr\b≥1, a -action with rankr, covering numberb and a simple spectrum. On the other hand, for any positive integersr, m with 1≤m≤r≤∞ we construct a -action with rankr and spectral multiplicitym.     

High repetition rate,Q-switched Ho:YAG laser resonantly pumped by a 20 W linearly polarized Tm: fiber laser

We describe an efficient, low-threshold, continuous-wave (CW) and Q-switched operation of a Ho:YAG laser resonantly, single-pass pumped by a 20 W linearly polarized narrow line width Tm: fiber laser at the wavelength of 1,908 nm. At room temperature for an output coupler of 30 % transmission, a maximum continuous-wave output power of 13.3 W for 18.9 W of absorbed pump power was achieved, corresponding to a slope efficiency of 73 %. In a quasi continuous-wave pumping regime, for several output couplers slope efficiencies of almost 82 % were observed. For a Q-switched operation, a Brewster-cut acousto-optic modulator was used. In a CW pumping regime, the pulse repetition frequency (PRF) was changed from 4 to 15 kHz. Under a Q-switched operation, the maximum output power of 12.25 W in relation to 15 kHz PRF was obtained; however, the maximum peak power of almost 250 kW at the PRF of 4 kHz was demonstrated. In the best case, for 4 kHz PRF, pulse energies of 2.18 mJ with a 8.8 ns FWHM pulse width (one of the shortest pulse durations observed in holmium-doped Q-switched lasers) were achieved. The laser operated at the wavelength of 2,090.23 nm with the FWHM line width of 0.95 nm. The beam quality factor of M ² was measured to be below 1.42 in both X and Y axis.     

Asymmetric synthesis of (−)-bissetone via a highly enantioselective hetero-Diels–Alder reaction

We demonstrate a new approach for the asymmetric synthesis of bissetone. The key reaction is the highly enantioselective hetero-Diels–Alder cycloaddition of triene 3 with ethyl glyoxylate catalyzed by readily available BINOL–Ti complexes. The HDA cycloadduct 4 was then transformed in five steps into O-protected bissetone (8) and its C5-epimer in good yield.     

A DFT and MP2 Study on the Molecular Structure and Vibrational Spectra of Halogenosubstituted Phosphoryl and Thiophosphoryl Compounds

The molecular geometrical parameters, rotational constants, dipole moments and vibrational infrared properties of a series of phosphoryl compounds (OPX _i Y _j Z _k , X, Y, Z = F, Cl, Br; i+ j + k = 3) and their thio analogs are predicted by density functional and MP2 calculations using the 6-311G(2d,2p) basis set. Both methods yielded similar results. The predicted molecular parameters and the vibrational Raman and infrared spectra agree well with the available experimental data. The Raman Scattering Activities (RSA) and depolarization ratios (Dep) of the molecules are obtained by DFT calculations. Considering the different substitution modes of various halogen atoms, the resultant changes in the geometrical and vibrational properties are discussed. Such studies permit detailed information to be obtained concerning unknown molecules and can define the guidelines for synthesizing molecules of particular characteristics.     

A simple electrostatic model of solvation for large molecules within the SCF MO theory

A very simple electrostatic model of solvation in which the solvent molecules are represented by point dipoles has been applied to simulate the hydration effect on molecular systems within the CNDO/2 method. The limitations of the model compared to the previous approaches as well as its feasible application to the study of tautomeric equilibria of cytosine and adenine in aqueous solution are discussed.     

Über die magnetische Untersuchung der Zersetzungsprodukte des Kobalt(II)-hexacyano-ferrates

Zusammenfassung Kobalt(II)-hexacyanoferrat wird in der Luft zersetzt und die Zersetzungsprodukte werden analytisch, durch Röntgenaufnahmen und magnetische Messungen identifiziert.Die Rückstände, deren Zusammensetzung von der Zersetzungstemperatur abhängt, bestehen hauptsächlich aus Co, Co₃O₄, -Fe₂O₃, -Fe₂O₃, CoFe₂O₄ und CoO.