5 research outputs found
Multiplicities in the length spectrum and growth rate of Salem numbers
We prove that multiplicities in the length spectrum of a non-compact
arithmetic hyperbolic orbifold of dimension have exponential
growth rate extending the analogous result for even dimensions of
Belolipetsky, Lal\'in, Murillo and Thompson. Our proof is based on the study of
(square-rootable) Salem numbers. As a counterpart, we also prove a refined
version of these asymptotic results, adapting the argument of G\"otze and
Gusakova for the case of square-rootable Salem numbers, to show that one can
not obtain a better estimate on the multiplicities using our approach.Comment: 14 page
Logarithmic algorithms for fair division problems
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient
Non-surjective Milnor patching diagrams
Milnor patching diagram is essentially the commutative square of rings, over
which gluing of finitely generated projective modules is possible in the
strongest sense. Necessary and sufficient conditions for a square to be Milnor
patching diagram were studied by Milnor, Beauville-Laszlo and Landsburg. We
relate this question to determinant-induced factorization in matrix rings to
construct a series of non-surjective Milnor patching diagrams, settling the
question of Landsburg, and make a step towards the classification of such
examples. Also we consider a possible generalization of the notion of Milnor
patching diagram to arbitrary subcategories of modules and obtain a
classification result for this setting.Comment: 13 page
Spline Approximation Method and Applications Thereof
Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio
Models and methods for subject specialization deepening of regional constructional enterprises by the mobile units` relocation
This article shows the amount of construction and installation works at the regional level that are formed according to the individual cluster territories, considering the specialization of the production development. For their implementation, it is necessary either to change the specialization of contracting capacities, or to use them with the consideration of the movement mobility in development zones