A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In scaling frame with dependent effective Planck mass these are regular. They become singular in Einstein fixed mass. This singularity arises since transformation of metric to is at crossing point vanishing field. No physical present solutions. Within general m...

singularity based on fractal and multifractal is a technique for detection of depletion and enrichment for geochemical exploration, while the index of vertical geochemical zonality (vz) of pb.zn/cu.ag is a practical method for exploration of blind porphyry copper mineralization. in this study, these methods are combined for recognition, delineation, and enrichment of vz in jebal- barez in the s...

In this paper, it is pointed-out that inverse problems arising in nonlinear control systems design such as state reconstruction and/or parameter estimation are naturally redundant. It is also shown that this redundancy can be used to enhance avoiding singularity heuristics. Some related algorithms are discussed and illustrated on a simple example of chemical reactors. These algorithms can be ad...

We give examples of reducible characteristic cycles for irreducible HarishChandra modules for U(p, q) by analyzing a four-dimensional singular subvariety of C. We relate this singularity to the Kashiwara-Saito singularity arising for Schubert varieties for GL(8,C) with reducible characteristic cycles, as well as recent related examples of Williamson. In particular, this gives another explanatio...

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and superrenormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higherderivative theories, when the poles of the propagator are real...

This paper is a continuation of two recent publications on crack growth in viscoelastic media. It provides further theoretical results for large strains that enable prediction opening displacement comparison with experimental data the region singularity. In order to achieve good agreement experiment it was necessary account far-field viscoelasticity. Additionally, found deformation throughout s...

In this paper we advance the program of using exceptional collections to understand the gauge theory description of a D-brane probing a Calabi-Yau singularity. To this end, we strengthen the connection between strong exceptional collections and fractional branes. To demonstrate our ideas, we derive a strong exceptional collection for every Y p,q singularity, and also prove that this collection ...

We propose causal fermion systems and Riemannian fermion systems as a framework for describing spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples like the Euclidean plane, the two-dimensional Minkowski space, a conical...