New static regular axially symmetric solutions of SU (2) Euclidean Yang-Mills theory are constructed numerically. They represent calorons having trivial Polyakov loop at spacial infinity. The solutions are labeled by two integers m, n. It is shown that besides known, charge one self-dual periodic instanton solution, there are other non-self dual solutions of the Yang-Mills equations naturally c...

Exponential dichotomy of a strongly continuous cocycle Φ is proved to be equivalent to existence of a Mañe sequence either for Φ or for its adjoint. As a consequence we extend some of the classical results to general Banach bundles. The dynamical spectrum of a product of two cocycles, one of which is scalar, is investigated and applied to describe the essential spectrum of the Euler equation in...

The SKA's design is driven by the needs of cutting-edge radio astronomy for sensitivity and spacial resolution. However its design is also driven by the desire to explore the transient radio Universe. In addition to pulsars, the SKA will be able to carry out high time resolution observations of several classes of known and predicted transient sources. Here we consider a selection of them, and d...

We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spacial dimension and unbounded time and space-dependent coefficients. The equation free term and the initial data are also allowed to grow. Under a nondegeneracy assumption, we consider the PDE solvability in the framework of the variational approach, and approximate in space the PDE probl...

In this paper we consider the homogenization of evolution problem associated with a jump process that involves three different smooth kernels govern jumps to/from parts domain. We assume spacial domain is divided into sequence two subdomains $$A_n \cup B_n$$ and have kernels, one controls from $$A_n$$ to , second $$B_n$$ third governs interactions between . Assuming $$\chi _{A_n} (x) \rightarro...

The tracking system of the CMS experiment, currently under construction at the Large Hadron Collider (LHC) at CERN (Geneva, Switzerland), will include a silicon pixel detector providing three spacial measurements in its final configuration for tracks produced in high energy pp collisions. In this paper we present the results of test beam measurements performed at CERN on irradiated silicon pixe...

In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in Hs, s > 2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric g, we manage to implement the commuting vector field approach to prov...

This paper discusses the trajectory following issue for redundant nonholonomic mobile modular manipulators. Dynamic model is established and an adaptive neural-network controller is developed to control the end-effector to follow a desired spacial trajectory. The proposed algorithm doesn’t need any priori dynamics and provides a new solution for stabilization of redundant robotic selfmotions. S...