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 $n \geqslant 4$ have exponential growth rate $$\langle g(L) \rangle \geqslant c \frac{e^{([n/2] - 1)L}}{L^{1 + \delta_{5, 7}(n) }},$$ 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