We study the nonlinear eigenproblem for monotone additively homogeneous maps f : Rn → Rn, and more generally, for monotone multiplicatively homogeneous maps on cones. When f is convex, monotone and additively homogeneous, we describe the nonlinear eigenspace of f using its subdifferential (or its tangent affine maps) [AG03]. This yields in particular an uniqueness result for the eigenvector of ...

A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a forward part, a numerical scheme is devised for solving this backward-forward stochastic system, and an ensemble of graphs representing the inertial manifold is co...

This work is concerned with existence of weak solutions to discontinuous stochastic differential equations driven by multiplicative Gaussian noise and sliding mode control dynamics generated by stochastic differential equations with variable structure, that is with jump nonlinearity. The treatment covers the finite dimensional stochastic systems and the stochastic diffusion equation with multip...

We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power– law dependence of the stochastic variable xa we show the way to phase transitions disorder–order and order–disorder. The governed equations for the order parameter and one-time correlator are obtained and investigated in details. The long–time asymptotes in th...

It is proved that if G = G1 ∗G3 G2 is free product of probability measure preserving s-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid G3, then the sofic dimension s(G) satisfies the equality s(G) = h(G01)s(G1) + h(G 0 2)s(G2) − h(G 0 3)s(G3) where h is the normalized Haar measure on G. Let G be a group. The sofic dimension of G is an asymptotic invariant that accoun...

Constructing maps of pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information in the U.S.: one is pollution measurements at a sparse set of about 50 monitori...

From the interpretation of Linear Logic multiplicative disjunction as the ε-product defined by Laurent Schwartz, we construct several models of Differential Linear Logic based on usual mathematical notions of smooth maps. This improves on previous results in [BET] based on convenient smoothness where only intuitionist models were built. We isolate a completeness condition, called k-quasi-comple...

We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems. AMS classification: 37F, 32H Key-words: multiplicative cocycle, sub-multiplicative cocycle, exceptional set

Abstract We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.