Brownian Motion on an Embedded Manifold as the Limit of Brownian Motions with Reflection in its Tubular Neighborhood

Mathematical Notes -     

Self-organization as the driving force for the evolution of the biosphere

In this paper we present a space-time model of urban ecosystems as conjugate active media. This approach is based on the representation of urban ecosystems as self-organizing systems; it aims at identifying the threshold values of control parameters and is considered promising in assessing system stability to internal and external fluctuations.     

Structure peculiarities of material formed by dynamic compacting of amorphous powders

Abstract

Structure and some properties of compacts dynamically produced from powders of Fe₈₂B₁₂Si₄C₂ and Co₅₉Ni₁₀Fe₅B_15.5Si_10.5 amorphous alloys are analyzed. The compacts of amorphous materials exhibit higher thermal stability as compared with that of starting powders.     

The Structure of LiNbO3:Tb Crystals with Various Chemical Compositions

Technical Physics - A series of LiNbO3:Tb crystals ([Tb] = 0.1–2.89 wt %) and nominally pure lithium niobate crystals of congruent (LiNbO3cong) and almost stoichiometric compositions...     

Stability of tungsten(VI) oxide dispersions in electrolyte solutions

The aggregation stability of tungsten oxide hydrosols is studied by the photometric and electrooptical methods. Coagulation thresholds determined in solutions of 1 : 1, 2 : 1, and 3 : 1 electrolytes obey the Schulze-Hardy rule. The coagulation is shown to occur by the barrier mechanism predominantly through adhering of small particles to large ones without considerable changes in the sizes of the latter.     

Effect of type of dislocation structure and grain size on the applicability of the Cottrell-Stokes law in alloys

A study is made of the applicability of the Cottrell-Stokes law in the solid solutions Cu-Al, Cu-Ga, and Cu-Ge, in the ordered alloys Ni₃Mn, Ni₃(MnCo), and Ni-Mn-Fe, and also in an aging alloy on an iron-nickel-chromium base. It is shown that the applicability of the Cottrell-Stokes law is greatly affected by the nature of the dislocation structure formed during stressing and also by the grain size.     

Interaction of nitroallyl with N-trimethylborazole

Conclusions An addition product of nitroallyl to N-trimethylborazole was obtained;, it proved to be a complex, formed on account of a donor-acceptor bond between the oxygen atom of the nitro group and boron.Translated from Izvestiya Akademii Nauk SSSR, Seria Khimicheskaya, No. 10, pp. 1881–1882, October, 1964     

The surface limit of Brownian motion in tubular neighborhoods of an embedded Riemannian manifold

We construct the surface measure on the space C([0,1],M) of paths in a compact Riemannian manifold M without boundary embedded into which is induced by the usual flat Wiener measure on conditioned to the event that the Brownian particle does not leave the tubular ε-neighborhood of M up to time 1. We prove that the limit as ε→0 exists, the limit measure is equivalent to the Wiener measure on C([0,1],M), and we compute the corresponding density explicitly in terms of scalar and mean curvature.