Related papers: Variations of star selection principles on Hypersp…
Given a family of varieties, the Euler discriminant locus distinguishes points where Euler characteristic differs from its generic value. We introduce a hypergeometric system associated with a flat family of very affine locally complete…
We show that Horrock's criterion for the splitting of vector bundles on $\PP^n$ can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool…
Given a coarse space $(X, \mathcal{E})$, we consider linear orders on $X$ compatible with the coarse structure $\mathcal E$ and explore interplays between these orders and macro-uniform selectors of $(X, \mathcal{E})$.
We give a review of the theory of random fields defined on the observable part of the Universe that satisfy the cosmological principle, i.e., invariant with respect to the 6-dimensional group $\mathcal{G}$ of the isometries of the time…
Each rule $f$ that assigns a vector $f(G)$ to an $(n+1)$-graph $G$ determines a class (or property) of $n$-manifold invariants. An invariant $v=v(M)$ is in this class if, for any triangulated manifold $|G|=M$, one has that $v(M)$ is a…
We describe distinctive stellar features indicating the presence of hyperons in neutron stars as compared to purely nucleonic systems. A strongly negative curvature of the mass-radius relation $R(M)$ is characteristic of hyperons, which can…
We prove a selection theorem for paraconvex-valued mappings defined on {\tau}-PF normal spaces. The method developed to prove this result is used to provide a general approach to such selection theorems.
In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that…
Efforts to understand the origin of the cosmological constant {\Lambda} and its observed value have led to consider it as a dynamical field rather than as a universal constant. Then the possibility arises that the universe, or regions of…
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $\left(\varphi_1, \varphi_2\right)-$convex function $g, $ with arbitrarily small norm, such that $f + g…
If the assumption that physical space has a trivial topology is dropped, then the Universe may be described by a multiply connected Friedmann-Lema\^{\i}tre model on a sub-horizon scale. Specific candidates for the multiply connected space…
In the present paper we demonstrate that there exists a new type of neutron stars in the tensor-multi-scalar theories of gravity. We call this new type of neutron stars topological neutron stars. In addition to the standard characteristics…
Variable star analysis and classification is an important task in the understanding of stellar features and processes. While historically classifications have been done manually by highly skilled experts, the recent and rapid expansion in…
The generalized (ordered) configuration spaces associated to a topological space $X$ are the spaces $\Delta_{\leq\ell}X^{m}:=\{(x_1,\ldots,x_{m})\in X^{m}\mid\#\{x_1,\ldots,x_{m}\}\leq \ell\}$ and…
It is shown that if a $T_2$ topological space contains an uncountable closed discrete set, then $\omega_1 \times (\omega_1 + 1)$ embeds as a closed subspace of $(CL(X),\tau_F)$, the hyperspace of nonempty closed subsets of $X$ equipped with…
Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own case - similarity shapes - the shape spaces are…
Let X be an exotic symmetric space G/H \times V, where G= GL(V) and H = Sp(V) for a symplectic vector space V over an algebraically closed field of odd characteristic. In our previous papers, character sheaves on X were constructed based on…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
This thesis concerns the compatibility of inhomogeneous cosmologies with our present understanding of the universe. It is a problem of some interest to find the class of all relativistic cosmological models which are capable of providing a…