Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by general Gaussian multiplicative noise, including cases of space–time white noise and white-colored with spatial covariance given Riesz kernel or bounded integrable function. We show that average over ball radius R converges, as tends to infinity, after suitable renormal...

We obtained analytical expressions considering a directed continuous-time quantum walk on infinite line using Bessel functions, expanding previous results in the literature, for general initial condition. derive equation probability distribution and show how to recover normal enhanced decay rates survival by adjusting phase factor of direction graph. Our result shows that mean standard deviatio...

General rigid bead-rod theory yields uniquely the relation between macromolecular architecture and complex viscosity. For this, it relies on analytical solution of general diffusion equation for small-amplitude oscillatory shear flow Bird et al. [Dynamics Polymeric Liquids, 2nd ed. (Wiley, New York, 1987), Vols. 1–2]. Unfortunately, this has yet to be solved any other field. In paper, we do so ...

We introduce a natural class of multicomponent local Poisson structures $$\mathcal P_k + \mathcal P_1$$ , where is bracket order one and P_k$$ homogeneous odd $$k$$ under the assumption that has Darboux coordinates (Darboux–Poisson bracket) nondegenerate. For such brackets, we obtain general formulas in arbitrary coordinates, find normal forms (related to Frobenius triples), provide description...

Stein’s method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation, the functional equation is a first-order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general Gaussian processes. Nourdin and Peccati (Probab. Theory Relat. Fields 145(1–2), 75...

Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...

Todorc̆ević’ trichotomy in the class of separable Rosenthal compacta induces a hierarchy tame (compact, metrizable) dynamical systems ( X , ...

Syntactic encapsulation is a relation between an expression and one of its sub-expressions, that constraints how the given sub-expression can be used throughout the reduction of the expression. In this paper, we present a class of systems of equations, in which the right-hand side of each equation is syntactically encapsulated in the left-hand side. This class is general enough to allow equatio...