We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

Using a distortion measure for the states emerging in self-organizing maps (SOMs) we mathematically analyse a recently proposed high-dimensional map formation model for ocular dominance patterns. We calculate critical values of parameters for ocular dominance states to occur, and we determine how the pattern layout depends on these parameters. The analysis reveals an increase of ocular dominanc...

A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α, β : A → A such that α(a)(bc) = (ab)β(c), for all a, b, c ∈ A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new ...

We incorporate auditory-based features into an unconventional pattern classification system, consisting of a network of spiking neurones with dynamical and multiplicative synapses. Although the network does not need any training and is autonomous, the analysis is dynamic and capable of extracting multiple features and maps. The neural network allows computing a binary mask that acts as a dynami...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

If M = Z, and G is a finite (nonabelian) group, then G is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation F : G − ←⊃ which commutes with all shift maps, and where nearby coordinates are combined together using the multiplication operator of G. We provide equivalent conditions for MCA to be group endomorphisms of G, and show how MCA on G inherit a natura...

This paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts. If such a subshift satisfies a certain condition, originally introduced by Boshernitzan, every locally constant SL(2,R)-valued cocycle is uniform. As a consequence, the corresponding Schrödinger operators exhibit Cantor spectrum of Lebesgue measure zero. An investigation of Boshernitza...

We examine some of the basic properties satisfied by Bloch’s cycle complexes for quasi-projective varieties over a field, and extend some of them to the cycle complex of a scheme of finite type over a regular dimension one base. We also give an extension to the simplicial spectra in the niveau tower of the cosimplicial scheme ∆∗ X . As applications, we show that the AtiyahHirzebruch spectral se...