We develop an extension of Bohmian mechanics by defining Bohm-like tra-jectories for (one or more) quantum particles in a curved background space-time containing a singularity. Part one, the present paper, focuses on timelike singu-larities, part two will be devoted to spacelike singularities. We use the timelike singularity of the (super-critical) Reissner–Nordström geometry as an example. Whi...

Parallel mechanisms frequently contain an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. By altering the mechanism through, for example, additional kinematic linkages, the singularity can be modi ed or even removed. Another approach is ...

Consider the following question. Given a suitable linear series L on a smooth surface S, how many curves in L have a given analytic or topological type of singularity? By “suitable” linear series with respect to a type of singularity, we mean that there are finitely many curves with the singularity in the linear series and their codimension is maximal. Our approach to this question is to expres...

String propagation on a three-dimensional Lorentzian string orbifold with a null singularity has been studied by Horowitz and Steif, and more recently by Liu, Moore and Seiberg. We analyze the target space as a classical gravitational background. The singularity becomes spacelike when an arbitrarily small amount of matter is thrown at the singularity. This can be seen directly by constructing a...

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

In this paper, we focus on the study of shearlet transform which isdened by using the hyperbolic functions. As a result we check an admissibilitycondition such that implies the reconstruction formula. To this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.

This is a review of my recent work. What kinds of combinations of singularities can appear in small deformation fibers of a fixed singularity? We consider this problem for hypersurface singularities on complex analytic spaces of dimension 2. Recall first that a connected Dynkin graph of type A, D or E corresponds to a surface singularity called a rational double point. (Durfee [3].) When the fi...

Via T-duality, a stack of unwrapped type 0 NS5-branes is transformed into a Kaluza-Klein monopole with An type singularity at its center. The spectrum of twisted modes at the singularity contains tachyonic modes. We show that, in certain parameter region, this tachyonic spectrum is completely reproduced as modes of the bulk tachyon field localized on a classical NS5-brane solution. In passing, ...

We propose a new cosmological scenario which resolves the conventional initial singularity problem. The space–time geometry has an unconventional time–like singularity on a lower dimensional hypersurface, with localized energy density. The natural interpretation of this singularity in string theory is that of negative tension branes, for example the orientifolds of type II string theory. Space–...

New Planck scale physics may solve the singularity problems of classical general relativity and may lead to interesting consequences for very early Universe cosmology. Two approaches to these questions are reviewed in this article. The first is an effective action approach to including the effects of Planck scale physics in the basic framework of general relativity. It is shown that effective a...