In this paper, we initiate the study of a new class of algebras, which we call cluster algebras. Before giving precise definitions, we present some of the main features of these algebras. For any positive integer n, a cluster algebra A of rank n is a commutative ring with unit and no zero divisors, equipped with a distinguished family of generators called cluster variables. The set of cluster v...

This article presents the results of a study microstructure sintered sample made alloy X13 electroerosive materials obtained in butyl alcohol. It has been established that during sintering by method spark plasma sintering, main elements on surface particles are Fe, Cr, Mn, and have generally regular spherical shape.

The article presents the results of a study wear resistance sintered specimens from electroerosive powder steel X13, obtained in butyl alcohol. friction coefficient was 0.950, width groove 455.9 µm, depth 6 factor sample 1.676x10-6 mm3 N-1m-1.

FAST MULTIPLICATION AND ITS APPLICATIONS DANIEL J. BERNSTEIN Abstra t. This survey explains how some useful arithmeti operations an be sped up from quadrati time to essentially linear time. x2. Produ t: the FFT ase x13. Sum of fra tions x3. Produ t: extension x11. Matrix produ t x14. Fra tion from ontinued fra tion x4. Produ t: zero-padding and lo alization 55 k k k k k k k k k k k k k x12. Pro...

Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X13-nYn (where n=1, 2, 3) are presented. The total energy, heat capacity, and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the pha...

The mechanical design considerations are discussed with respect to the currently installed X-13 and future X-29 MGU. Comparisons to the previous 2 generations of variable small-gap undulator evolution in the NSLS X-ray ring are made and design improvements noted. The design requirements and mechanical difficulties for holding, positioning and driving the magnetic arrays are explored. Structural...

PLAGIOCLASE. Hejiu Hui, Yunbin Guan, Yang Chen, Anne H. Peslier, Youxue Zhang, Yang Liu, George R. Rossman, John M. Eiler, Clive R. Neal, Department of Civil & Environmental Engineering & Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, Jet Propulsion Laboratory, California Inst...