A perturbation matrix A = A is considered, where A 2 IR and 0 2 IR. The matrix A is singular i A contains a real singular matrix. A problem is to decide if A is singular or nonsingular, a NP-hard problem. The decision can be made by the computation of the componentwise distance to the nearest singular matrix de ned on the basis of the real spectral radius, and by the solution of 4 eigenvalue pr...

The paper describes the arriving, the probable and the inevitable, emerging through the exponential technological development, particularly the informational one (IT), and by the new concepts of Kurzweil’s singularity of the strong artificial intelligence (AI) on the one side and by the recursiveness of author’s informational consciousness (IC) on the other. A comparison between the criteria of...

Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended. Is such progress avoidable? If not to be avoided, can events be guided so that we may survive? These questions are investigated. Some possible answers (and some further dangers) are presented. _What is The Singularity?_ The acceleration of technological progre...

In this paper, we apply the microlocal analysis to study the singularity structure of the two-point function in a supersymmetric model formulated in superspace language.

In this paper we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields can be applied independently that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allows to study monodromic degenerate singu...

We deal with the definition of superdistributions on superspace over a Grassmann-Banach algebra and the extension of the Hörmander's description of the singularity structure (wavefront set) of a distribution to include the supersymmetric case.

For each n ∈ N, n ≥ 2 we prove the existence of a positive solution of the singular discrete problem 1 h2 ∆uk−1 + f(tk, uk) = 0, k = 1, . . . , n− 1, ∆u0 = 0, un = 0, where T ∈ (0,∞), h = T n , tk = hk, f : [0, T ] × (0,∞) is continuous and has a singularity at x = 0. We prove that for n → ∞ the sequence of solutions of the above discrete problems converges to a solution y of the corresponding ...

We present a consistent framework that enables us to understand the big bang singularity of our Universe.

The singularity space consists of all germs (X, x), with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given by the order to which infinitesimal neighborhoods agree after base change. In other words, the classification of singularities up to analytic extensions of scalar...

We study the formation of black strings from a gravitational collapse of cylindrical dust clouds in the three-dimensional low-energy string theory. A new junction condition for the dilaton as well as two junction conditions for metrics and extrinsic curvatures between both regions of the clouds is presented. As a consequence, it is found that the collapsing dust cloud always collapses to a blac...