100 research outputs found
On finite functions with non-trivial arity gap
Given an -ary
valued function , denotes the minimal number of essential
variables in which become fictive when identifying any two distinct
essential variables in .
We particularly solve a problem concerning the explicit determination of
-ary
valued functions with . Our methods yield
new combinatorial results about the number of such functions.Comment: 17 pages, Int. Conf. Algebraic and Combinatorial Coding Theory,
ACCT2008, June 16 - Sunday 22, 2008, Pamporovo, BULGARI
Hierarchy of boundary driven phase transitions in multi-species particle systems
Interacting systems with driven particle species on a open chain or
chains which are coupled at the ends to boundary reservoirs with fixed particle
densities are considered. We classify discontinuous and continuous phase
transitions which are driven by adiabatic change of boundary conditions. We
build minimal paths along which any given boundary driven phase transition
(BDPT) is observed and reveal kinetic mechanisms governing these transitions.
Combining minimal paths, we can drive the system from a stationary state with
all positive characteristic speeds to a state with all negative characteristic
speeds, by means of adiabatic changes of the boundary conditions. We show that
along such composite paths one generically encounters discontinuous and
continuous BDPTs with taking values depending on
the path. As model examples we consider solvable exclusion processes with
product measure states and particle species and a non-solvable
two-way traffic model. Our findings are confirmed by numerical integration of
hydrodynamic limit equations and by Monte Carlo simulations. Results extend
straightforwardly to a wide class of driven diffusive systems with several
conserved particle species.Comment: 12 pages, 11 figure
Uniform growth of groups acting on Cartan-Hadamard spaces
Let be an -dimensional simply connected manifold of pinched sectional
curvature . There exist a positive constant such
that for any finitely generated discrete group acting on , then
either is virtually nilpotent or the algebraic entropy
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