Related papers: On densities of box products
The evolution of marginally bound supercluster-like objects in an accelerating LambdaCDM Universe is followed, by means of cosmological simulations, from the present time to an expansion factor a = 100. The objects are identified on the…
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We…
By utilizing large-scale graph analytic tools implemented in the modern Big Data platform, Apache Spark, we investigate the topological structure of gravitational clustering in five different universes produced by cosmological $N$-body…
In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy…
We analyze the structure and connectivity of the distinct morphologies that define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF), we dissect the matter distribution of a cosmological $\Lambda$CDM N-body computer…
A new example of $(2+1)$-dimensional Zollfrei metric, with the topology $R^2 \times S^1 $, is presented. This metric is readily obtained from the celebrated $(3+1)$- dimensional rotating G\"odel universe $G_{3,1}$. This is because $G_{3,1}$…
In a Brans-Dicke (BD) cosmological model, the energy density associated with some scalar field decreases as $\displaystyle a^{{-2}(\frac{\omega_{o}+ {\frac12}%}{\omega_{o}+1})} $ with the scale factor $a(t)$ of the Universe, giving a matter…
In the standard cosmological model, the Universe consists mainly of two invisible substances: vacuum energy with constant mass-density rho_v=\Lambda/(8pi G) (where Lambda is a `cosmological constant' originally proposed by Einstein and G is…
The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
The dimensionality of vortical structures has recently been extended beyond two dimensions, providing higher-order topological characteristics and robustness for high-capacity information processing and turbulence control. The generation of…
The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and…
We analyze the effect of higher order viscosity corrections in a spatially homogeneous and isotropic universe. The viscous effects are modeled by introducing a second-order term to the energy density in the equation of state and on the…
We analyse the spacetime structure of the global vortex and its maximal analytic extension in an arbitrary number of spacetime dimensions. We find that the vortex compactifies space on the scale of the Hubble expansion of its worldvolume,…
We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G,…
The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology $\sigma(X,X')$ of a locally convex space $X$, in…
We show that unlike the usual topologies the $g$-topologies are closed with respect to the Cartesian products. Moreover, we bring much detailed explanations some examples of concepts related the statistical metric spaces.
We consider the problem of minimal volume vector fields on a given Riemann surface, specialising on the case of $M^\star$, that is, the arbitrary radius 2-sphere with two antipodal points removed. We discuss the homology theory of the unit…