Central Limit Theorem for a Class of Nonhomogeneous Random Walks

A spatially nonhomogeneous random walk _t on the grid =^m X ⁿ is considered. Let _t ⁰ be a random walk homogeneous in time and space, and let _t be obtained from it by changing transition probabilities on the set A= X ⁿ, || < , so that the walk remains homogeneous only with respect to the subgroup ⁿ of the group . It is shown that if >m 2 or the drift is distinct from zero, then the central limit theorem holds for _t.     

Invariance principle for nonhomogeneous random walks on the grid ℤ1

A nonhomogeneous random walk on the grid ℤ¹ with transition probabilities that differ from those of a certain homogeneous random walk only at a finite number of points is considered. Trajectories of such a walk are proved to converge to trajectories of a certain generalized diffusion process on the line. This result is a generalization of the well-known invariance principle for the sums of independent random variables and Brownian motion. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 459–472, September, 1999.     

Simple synthesis of O-benzylidene derivatives of sugars

Conclusions A convenient method was proposed for obtaining cyclic O-benzylidene acetals of sugars.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2160–2161, September, 1977.     

Separate quantitative determination of hexoses and pentoses employing o-toluidine reagent

Conclusions A spectrophotometric method was proposed for the separate determination of hexoses and pentoses when jointly present, which is based on the difference in the absorption spectra of the reaction products of these sugars with o-toluidine reagent.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 877–880, April, 1974.