The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2. In Part 1, we prove...

We study operator Lyapunov equations in which the innnitesimal generator is not necessarily stable; but it satisses a spectrum decomposition assumption and it has at most nitely many unstable eigenvalues. Under mild conditions; these have unique self-adjoint solutions. We give conditions under which the number of negative eigenvalues of this solution equals the number of unstable eigenvalues of...

Abstract: A set of conditions are found for stabilization of unstable processes using relay feedback. The relay-stabilized process will exhibit limit cycles which can then be used to obtain parameters of the process. In this paper, we explore the solution of firstand secondorder processes containing one unstable eigenvalue and time delay. The resulting necessary conditions found turn out to be ...

BACKGROUND Studies of the normal zone in high-temperature superconducting wires are extremely important for power applications, such as fault current limiters, motors, cables etc. We studied the temperature distribution and normal domain propagation in high-temperature superconducting YBCO tape with highly resistive substrate. FINDINGS For applied voltages exceeding a certain threshold value ...

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the in...

We investigate the spatially inhomogeneous decay of an unstable D-brane and construct an asymptotic solution which describes a codimension one D-brane and the tachyon matter in boundary string field theory. In this solution, the tachyon matter exists around the lower-dimensional D-brane.

Some new, efficient, and numerically stable algorithms for the recursive solution of matrix problems arising in optimal beamforming and direction finding are described and analyzed. The matrix problems considered are systems of linear equations and spectral decomposition. While recursive solution procedures based on the matrix inversion lemma may be unstable, ours are stable. Furthermore, these...

We discuss axisymmetric force-free pulsar magnetospheres with magnetically collimated jets and a disk-wind obtained by numerical solution of the pulsar equation. This solution represents an alternative to the quasi-spherical wind solutions where a major part of the current flow is in a current sheet which is unstable to magnetic field annihilation.

Many models for multi-fluid flow result in equations which fail to be hyperbolic. One example is one-dimensional flow of an incompressible two-phase fluid. In the simplest model, the principal part of the differential operator has characteristics with nonzero imaginary part for any state of the fluid which contains both phases. Thus, the linearized equations are catastrophically unstable. This ...

1. introduction adding lime to increase the geotechnical characteristics of fine-grained soils, to achieve different goals always been done from ancient time. there are many techniques for stabilizing unstable slopes, among them lime treatment is a quick, simple and cost-effective operation that can be incorporated into any unstable slopes. some scientific techniques of soil treatment have been...