Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Unimodular lattices with long shadow

Let L be an odd unimodular lattice of dimension n with shadow n−16. If min(L)?3 then dim(L)?46 and there is a unique such lattice in dimension 46 and no lattices in dimensions 44 and 45. To prove this, a shadow theory for theta series with spherical coefficients is developed.     

Kinetics and mechanism of free-surface vaporization of zinc, cadmium and mercury oxides analyzed by the third-law method

On the basis of critical comparison of experimental and theoretical values of the E parameter and investigation of the retardation effect of oxygen on the evaporation rate of ZnO, CdO and HgO, it was concluded that the dissociative evaporation of ZnO and HgO proceeds with releasing of atomic oxygen (O) as a primary product of decomposition. By contrast, the mechanism of dissociative evaporation of CdO corresponds to the equilibrium reaction with releasing of molecular oxygen (O₂) as a primary product of decomposition. As was shown, this difference in mechanisms is not related with interatomic OO distances in these oxides. From the analysis of crystal structure for 12 different oxides, which evaporate with releasing of atomic oxygen, and for 13 compounds, which evaporate with releasing of molecular oxygen, it was revealed that the first mechanism is observed for all oxides with the cubic crystal structure. It was proposed that a decisive role in this difference belongs to a local symmetry in the position of O atoms.     

Canonical Structure and Symmetries of the Schlesinger Equations

The Schlesinger equations S _(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m × m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations S _(n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.     

On Uniform Boundedness and Uniform Asymptotics for Orthogonal Polynomials on the Unit Circle

The known conditions due to G. Baxter, Ya. L. Geronimus, and B. L. Golinskii which guarantee the uniform boundedness and/or uniform asymptotic representation for orthonormal polynomials on the unit circle are under consideration. We show that these conditions are in general not necessary. We discuss the relation between the orthonormal polynomials on the unit circle, the best approximations, and absolutely convergent Fourier series.     

Mechanism of the thermal decomposition of nitrates from graphite furnace mass spectrometry studies

A basically new mechanism of the thermal decomposition of solids is proposed to explain the mass spectral observations of gaseous molecules of CoO, CuO, Cu₂O, NiO, PbO and Mg(OH)₂ during the low-temperature decomposition of the anhydrous and hydrated nitrates of these metals. The mechanism consists of two stages: congruent gasification of all reaction products irrespective of their saturated vapor pressure and subsequent condensation of the low-volatility species (oxides and hydroxides). The partial pressures of these species at the appearance temperatures calculated from this theory for the first stage of the process (1–50 mPa) are in agreement with the detection limits of the quadrupole mass spectrometers used in these experiments. The proposed mechanism is supported by other available data obtained by thermal analysis.     

A one‐dimensional CdII coordination polymer: catena‐poly[cadmium(II)‐bis(μ‐6‐methylpicolinato)]

In the title compound, [Cd(C₇H₆NO₂)₂]_n, the Cd^II ion has a distorted octahedral geometry. The 6‐methylpyridine‐2‐carboxylate anions are perpendicular to one another and act as bidentate and bridging ligands. Two carboxylate O atoms bridge the Cd^II ions, forming centrosymmetric dinuclear units. These units are further connected via carboxylate O atoms into a one‐dimensional polymeric chain which extends in the [100] direction.     

Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of the equilibrium measure for a wide class of parameter functions of the process. This formula proves the conjecture stated in [5] for the above class of processes. The method used goes back to A. Khintchine.     

Solid-phase extraction on alkyl-bonded silica gels in inorganic analysis.

Solid-phase extraction (SPE) is an effective tool for the preconcentration of trace elements and their separation from various sample constituents. Octadecyl and other alkyl-bonded silica gels are most widely used for these purposes. The fundamentals of the SPE of inorganic ions are reviewed and compared with those of related techniques (liquid-liquid extraction and reversed-phase liquid chromatography). The extraction of ions in the form of chelate compounds, inorganic salts solvated by neutral reagents, and ion-pair compounds is considered. Numerous applications of SPE to the separation and preconcentration of different elements and their species, including on-line combinations with instrumental determination techniques, are described and tabulated.