Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for decoding, resembling the decoding of Reed-Solomon codes and aligns with decoding by error correcting pairs. We have used the multiplicative structure on toric codes to c...

The multiplicative fragment of linear logic has found a number of applications in computational linguistics: in the "glue language" approach to LFG semantics, and in the formulation and parsing of various categorial grammars. These applications call for efficient deduction methods. Although a number of deduction methods for multiplicative linear logic are known, none of them are tabular methods...

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

We propose an explicit, easily-computable algebraic criterion for approximate null-controllability of a class of general piecewise linear switch systems with multiplicative noise. This gives an answer to the general problem left open in [13]. The proof relies on recent results in [4] allowing to reduce the dual stochastic backward system to a family of ordinary differential equations. Second, w...

Oseledets’ celebrated Multiplicative Ergodic Theorem (MET) [V.I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210.] is concerned with the exponential growth rates of vectors under the action of a linear cocycle on Rd. When the linear actions are invertible, the MET guarantees an almost-everywhere poi...