Disjoinable Lagrangian spheres and dilations

We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by adding quadratic terms) sufficiently often.     

Incompressible quantum liquids and new conservation laws

In this Letter, we investigate a class of Hamiltonians which, in addition to the usual center-of-mass momentum conservation, also have center-of-mass position conservation. We find that, regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is p/q, where and are coprime integers. Interestingly, the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely, the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.     

Die Kristallstruktur von Lithiummesitolat [{LiOC6H2-2,4,6-(CH3)3}4(THF)3]

X-Ray Structure of [{LiOC₆H₂-2,4,6-(CH₃)₃}₄(THF)₃] The title compound crystallized from a THF/OEt₂ solution. Its crystal structure (monoclinic, P2₁/c, a = 21.362(3), b = 13.441(2), c = 17.188(2) Å, β = 98.39(1)°, Z = 4, R = 0,0911, wR² = 0,2562) is built up by cuban-like tetrameric units. Three of the four Li cations attain a coordination number of four by binding to an additional THF molecule. Li(4) without THF coordination has a short distance to one ortho-methyl group (Li(4)…C(27) 2.669(10) Å). The Li–O_ph bonding distances vary from 1.869(10) to 2.051(10) Å (average 1.97 Å); the average bonding distance for Li–O_THF is 2.012(10) Å. Averaged bonding angles for Li–O_ph–Li′ and O_ph–Li–O′_ph amount to 84.4(4)° and 95.4(4)°, respectively. The Li…Li distances significantly differ from each other. They range from 2.556(12) to 2.739(11) Å (average 2.65(1) Å).     

The crystal and molecular structure of 1,12-dibromododecane,C12H24Br2

The α,ω-dihaloalcanes could serve as model compounds for polyethylenes in further studies of infrared and Raman-spectra. The 1,12-dibromododecane, belonging to this class of compounds, has the monoclinic space group P 2₁/a with the cell parameters a = 24.8 Å, b = 5.40 Å, c = 5.50 Å, β = 99°, Z = 2. The preparation of crystals was very difficult. The crystal finally used gives only few and bad X-ray data measured by film method (equiinclination Weissenberg). Therefore the accuracy of the structure determination is not high, but the result is reliable and has model character for related compounds. All molecules are ordered with their long molecular axes parallel to the (401) planes of the unit cell. There are alternating plane layers of bromine atoms on the one hand and aliphatic parts of the molecules on the other hand, both parallel to the (100)-planes. This molecular arrangement explains well the spectroscopic and crystal optical properties of the structure and also of related compounds like 1,10-dibromodecane and 1,18-dibromooctadecane.     

Initial oxidation of Al films investigated by AES,work function and gravimetric measurements

The beginning oxidation of evaporated Al films was measured under UHV conditions by means of AES, gravimetric oxygen uptake and work function changes. The high resolution of our quartz oscillator microbalance (Δm = 7 × 10^-11g/cm² with a time response <1 s) allowed to separate two reaction rates, a logarithmic one for an oxygen uptake <6 × 10^-8g/cm² and an inverse-logarithmic one for Δm > 7.5 × 10^-8g/cm². At room temperature a decrease of work function with an equilibrium value of -0.75 eV (oxygen uptake 9.10^-8g/cm²) with increasing oxidation was observed. This is interpreted as incorporation of oxygen and diffusion of Al^δ+ ions to the surface. But at T = 80 K an increase of work function with a maximum value of 0.5 eV was found. This is attributed to adsorbed oxygen because the incorporation is much slower at this temperature. The AES of pure Al is characterized by the low energy 64 eV peak. The decrease of the 64 eV peak and the increase of two new peaks at 50 and 37.5 eV during the oxidation were measured as a function of oxygen uptake and attributed to the change of electron density of states in the conduction band of aluminum.     

The Molecular and Crystal Structure of p-methyl-phenyl-glyoxyacid-p-chloranilide

Using X-ray crystal structure analysis of the title compound the positions of all the atoms (including all H atoms) in the monoclinic unit cell with the parameters a = 13.90₀ Å, b = 5.13₈ Å, c = 17.95₆ Å and β = 91.05° and the space group P 2₁/n were localized. The existence of an intramolecular N—H(N)…︁ O(1)-bridge was inferred, whose H-bridge acceptor predominantly is the π-electron density of the carbonyl group. At the same time the H(N) atom participates in the intermolecular bridge N H(N)…︁ O′(1) to the symmetry-equivalent neighbouring molecule. H-bridge-like interactions of the two phenyl hydrogen atoms H(6) and H(15) to the carbonyl oxygen O(2) have also been inferred from the torsion angles.     

Generalized symmetric planes

In this paper we relate the theory of stable planes to the theory of generalized symmetric spaces in the sense of differential geometry where the symmetries may be of arbitrary order. This leads to the notion of a generalized symmetric plane. We assign to every generalized symmetric plane an associated infinitesimal model and show that the associated infinitesimal model essentially determines a generalized symmetric plane up to global isomorphism. In particular, every generalized symmetric plane with an abelian group of transvections is a topological translation plane.