A three-dimensional lattice gas approximation for multilayer adsorption

A three-dimensional lattice gas approximation for multilayer adsorbates is substantiated on the basis of statistical physics. In addition, some problems of equilibrium thermodynamics and kinetics are formulated, and a number of approximations are derived. A detailed kinetic theory of thin film growth, which is complementary to the applied approaches based on phenomenological models, thermodynamics of nonequilibrium processes, and solid medium and lattice gas models, is developed.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 1, pp. 130–148, October, 1995.     

Flips and the Hilbert scheme over an exterior algebra

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.     

Integration of differential forms on manifolds with locally-finite variations. II

In part I of the paper, we have defined n-dimensional C⁰-manifolds in ℝⁿ(m ≥ n) with locally-finite n-dimensional variations (a generalization of locally-rectifiable curves to dimensionn > 1) and integration of measurable differential n-forms over such manifolds. The main result of part II states that an n-dimensional manifold that is C¹-embedded into ℝ^m has locally-finite variations and the integral of a measurable differential n-form defined in part I can be calculated by the well-known formula. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 66–85.     

Wild tiles in ℝ<Superscript>3</Superscript> with spherical boundaries

Wildly embedded tiles in ℝ³ with spherical boundary are discussed. The construction of the topologically complicated, crumpled cube tiles is reviewed. We construct an infinite family of wildly embedded, cellular tiles with Fox-Artin-type wild points. Finally, a condition on the set of wild points on a cellular tile is given to show that certain wild cells cannot be tiles. Several observations are recorded for further investigations. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 203–211, 2005.     

Lipschitz classes on local fields

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).     

Solvothermal Synthesis of Molybdenum Disulfide Hollow Spheres Modified by Cyanex 301 in Water–Ethanol Medium

Hollow spherical molybdenum disulfide has been successfully synthesized via a solvothermal method using Cyanex 301 as sulfur source and modification agent. The hollow spheres are characterized by transmission electron microscopy, scanning electron microscopy, X-ray diffraction and Energy-Dispersive X-ray analysis. The influences of reaction conditions are also discussed while a mechanism is proposed to explain the formation of the peculiar morphology.