Related papers: The Non-Existent Complex 6-Sphere
Unique features of particle orbits produce novel signatures of gravitational observable phenomena, and are quite useful in testing compact astrophysical objects in general relativity or modified theories of gravity. Here we observe a…
New solution for two interpenetrating universes is found. Higher derivative gravity acting in 6-dimensional space is the basis of the study that allows to obtain stable solution without introducing matter of any sort. Stability of the…
We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.
Wormholes are hypothetical topologically-non-trivial structures of the spacetime. From the theoretical point of view, the possibility of their existence is challenging but cannot be ruled out. This article is a compact and non-exhaustive…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
A calculation of the no-boundary wave-function of the universe is put forward for a spacetime with negative curvature. A semi-classical Robertson-Walker approximation is attempted and two solutions to the field equations, one Lorentzian and…
An attempt is made in order to clarify the so called regular black holes issue. It is revisited that if one works within General Relativity minimally coupled with non linear source, mainly of electromagnetic origin, and within a static…
The remarkably long-standing problem of cryptography is to generate completely secure key. It is widely believed that the task cannot be achieved within classical cryptography. However, there is no proof in support of this belief. We…
The concept of dark matter in the Universe and its components has been discussed in the 1930s by several authors, and in particular by Oort (1932) and Zwicky (1933). However, it is only in the 1970s that the existence of dark matter was…
The quantum plasma theory has flourished in the past few years without much regard to the physical validity of the formulation or its connection to any real physical system. It is argued here that there is a very limited physical ground for…
Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at…
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…
Recently, the authors of the present work (together with M. N. Kolountzakis) introduced a new version of the non-commutative Delsarte scheme and applied it to the problem of mutually unbiased bases. Here we use this method to investigate…
The actual existence of collections of universes -- multiverses -- is strongly suggested by leading approaches to quantum cosmology, and has been proposed earlier as an attractive way to explain the apparent fine-tuned character of our…
We consider the proposition that multiple universes exist by reviewing the various manifestations. In recent years, this idea has been elevated from science fiction and introduced in separate guises as an explanation for coincidence…
We make the case for the existence of a, hitherto unknown and unobserved, hierarchy of ever more compact cosmic objects in the universe. This hypothesis is based on i) the assumption of "elementary" particle sub-constituents on several…
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we…
In an Euclidean $d$-space, the container problem asks to pack $n$ equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\geq 2$ we show that solutions to the container problem can…
We explain an error in our paper "A smooth foliation of the 5-sphere by complex surfaces", Ann. Math 156 (2002), p.915-930.
In this paper we prove a topological nonrealizability theorem: certain classes of graded $BP_*$-modules are shown to never occur as the $BP$-homology of a spectrum. Many of these $BP_*$-modules admit the structure of $BP_*BP$-comodules,…