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Numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. The main result is the construction of a four-dimensional simple unitary algebra with fractional PI-exponent strictly less than its…

Noncommutative gravity in three dimensions with no cosmological constant is reviewed. We find a solution which describes the presence of a torsional source.

Noncommutative three-dimensional gravity can be described in terms of a noncommutative Chern-Simons theory. We extend this structure and also propose an action for gravitational fields on an even dimensional noncommutative space. The action…

The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the…

In (Phys. Rev. D 62, 081501, 2000) we proposed a unified approach to description of continuous and discrete spacetime based on nonassociative geometry and described nonassociative smooth and discrete de Sitter models. In our paper we give…

We investigate several boundedness properties of function spaces considered as uniform spaces.

We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on $\ell_\infty.$ As a consequence we get that every dual Banach space containing…

Let $(X,d)$ be a compact metric space, $f:X\rightarrow X$ be a continuous transformation with the specification property. we consider non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is…

Generalizing a theorem of Ph. Dwinger, we describe the partially ordered set of all (up to equivalence) zero-dimensional locally compact Hausdorff extensions of a zero-dimensional Hausdorff space. Using this description, we find the…

We consider quantum field theory in de Sitter space, focusing on the cases of scalars, spin 1/2 fields, and symmetric and anti-symmetric tensor fields of arbitrary spin. The free field equations in global coordinates can be reduced to a one…

Let $X$ be a (real or complex) infinite dimensional linear space. We establish conditions on a homogeneous polynomial $P$ on $X$ so that, if $W$ is any finite dimensional subspace of $X$ on which $P$ vanishes, then $P$ vanishes on an…

We present a family of examples of two dimensional, hyperbolic complex manifolds whose envelopes of holomorphy are not hyperbolic.

In this paper, we study CAT(0) spaces with non-locally connected boundary. We give some condition of a CAT(0) space whose boundary is not locally connected.

A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.

We give an example of an aleph-zero-categorical theory which is not G-compact. The countable model of this theory does not have AZ-enumerations.

We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.

Let $X$ be a proper metric space and let $F$ be a finite group acting on $X$ by isometries. We show that the asymptotic dimension of $F\backslash X$ is the same as the asymptotic dimension of $X$.

We investigate two simplified non-singular cyclic models with a negative time-varying cosmological constant to represent the non-conventional mechanism of negative cosmological constant expected to address the late-time cosmic acceleration.…

We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency.

In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying the Gromov's $4$-point condition) while the intersection of any two metric balls therein does not either "look like" a ball or has…